Exhibit 10.4

   

  March
      4, 2021

   

  Arrowroot
      Acquisition Corp.

  

  4553
      Glencoe Ave, Suite 200

  

  Marina
      Del Rey, CA 90292

   

  Re:
        Initial Public Offering

   

  Ladies
      and Gentlemen:

   

  This
      letter (this “Letter Agreement”) is being delivered to you in accordance with the Underwriting Agreement
      (the “Underwriting Agreement”) entered into by and between Arrowroot Acquisition Corp., a Delaware corporation
      (the “Company”), and Cantor Fitzgerald & Co., as representative (the “Representative”)
      of the several underwriters (each, an “Underwriter” and collectively, the “Underwriters”),
      relating to an underwritten initial public offering (the “Public Offering”), of up to 28,750,000 of
      the Company’s units (including up to 3,750,000 units that may be purchased to cover over-allotments, if any) (the “Units”),
      each comprised of one share of the Company’s Class A common stock, par value $0.0001 per share (the “Class A
          Common Stock”), and one-half of one redeemable warrant. Each whole warrant (each, a “Warrant”)
      entitles the holder thereof to purchase one share of Class A Common Stock at a price of $11.50 per share, subject to adjustment
      as described in the Prospectus (as defined below). The Units will be sold in the Public Offering pursuant to a registration statement
      on Form S-1 and prospectus (the “Prospectus”) filed by the Company with the U.S. Securities and Exchange
      Commission (the “Commission”) and the Units have been approved for listing on the Nasdaq Capital Market.
      Certain capitalized terms used herein are defined in paragraph 11 hereof.

   

  In
      order to induce the Company and the Underwriters to enter into the Underwriting Agreement and to proceed with the Public Offering
      and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, each of Arrowroot
      Acquisition LLC (the “Sponsor”) and the undersigned individuals, each of whom is a member of the Company’s
      board of directors and/or management team (each of the undersigned individuals, an “Insider” and collectively,
      the “Insiders”), hereby agrees with the Company as follows:

   

  1.
      The Sponsor and each Insider agrees that if the Company seeks stockholder approval of a proposed Business Combination, then in
      connection with such proposed Business Combination, it, he or she shall (i) vote any shares of Common Stock (as defined below)
      owned by it, him or her in favor of any proposed Business Combination and (ii) not redeem any shares of Common Stock owned by
      it, him or her in connection with such stockholder approval. If the Company seeks to consummate a proposed Business Combination
      by engaging in a tender offer, the Sponsor and each Insider agrees that it, he or she will not sell or tender any shares of Common
      Stock owned by it, him or her in connection therewith.

   

  2.
      The Sponsor and each Insider hereby agrees that in the event that the Company fails to consummate a Business Combination within
      24 months from the closing of the Public Offering, or such later period approved by the Company’s stockholders in accordance
      with the Company’s amended and restated certificate of incorporation (as it may be amended from time to time, the “Charter”),
      the Sponsor and each Insider shall take all reasonable steps to cause the Company to (i) cease all operations except for the purpose
      of winding up, (ii) as promptly as reasonably possible but not more than ten business days thereafter, redeem 100% of the shares
      of Class A Common Stock sold as part of the Units in the Public Offering (the “Offering Shares”), at
      a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account (as defined below), including
      interest earned on the funds held in the Trust Account (which interest shall be net of taxes payable and up to $100,000 of interest
      to pay dissolution expenses), divided by the number of then outstanding Offering Shares, which redemption will completely extinguish
      all Public Stockholders’ rights as stockholders (including the right to receive further liquidating distributions, if any),
      and (iii) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining
      stockholders and the Company’s board of directors, liquidate and dissolve, subject in each case to the Company’s obligations
      under Delaware law to provide for claims of creditors and other requirements of applicable law. The Sponsor and each Insider agrees
      to not propose any amendment to the Charter to modify the substance or timing of the Company’s obligation to redeem 100%
      of the Offering Shares if the Company does not complete a Business Combination within the required time period set forth in the
      Charter or with respect to any other material provisions relating to stockholders’ rights or pre-initial business combination
      activity, unless the Company provides its Public Stockholders with the opportunity to redeem their Offering Shares upon approval
      of any such amendment at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account,
      including interest earned on the funds held in the Trust Account (which interest shall be net of taxes payable and up to $100,000
      of interest to pay dissolution expenses), divided by the number of then outstanding Offering Shares.

   

  
     

    
      

    

  

   

  The
      Sponsor and each Insider acknowledges that it, he or she has no right, title, interest or claim of any kind in or to any monies
      held in the Trust Account or any other asset of the Company as a result of any liquidation of the Company with respect to the
      Founder Shares held by it, him or her. The Sponsor and each Insider hereby further waives, with respect to any shares of Common
      Stock held by it, him or her, if any, any redemption rights it, he or she may have in connection with (A) the consummation of
      a Business Combination, including, without limitation, any such rights available in the context of a stockholder vote to approve
      such Business Combination, or (B) a stockholder vote to approve an amendment to the Charter to modify the substance or timing
      of the Company’s obligation to redeem 100% of the Offering Shares if the Company has not consummated a Business Combination
      within the time period set forth in the Charter or with respect to any other material provisions relating to stockholders’
      rights or pre-initial business combination activity or in the context of a tender offer made by the Company to purchase Offering
      Shares (although the Sponsor, the Insiders and their respective affiliates shall be entitled to redemption and liquidation rights
      with respect to any Offering Shares it or they hold if the Company fails to consummate a Business Combination within the time
      period set forth in the Charter).

   

  3.
      Notwithstanding the provisions set forth in 7(a) and (b) below, during the period commencing on the effective date of the Underwriting
      Agreement and ending 180 days after such date, the Sponsor and each Insider shall not, without the prior written consent of the
      Representatives, (i) sell, offer to sell, contract or agree to sell, hypothecate, pledge, grant any option to purchase or otherwise
      dispose of or agree to dispose of, directly or indirectly, or establish or increase a put equivalent position or liquidate or
      decrease a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange
          Act”) and the rules and regulations of the Commission promulgated thereunder, with respect to any Units, shares
      of Common Stock, Founder Shares, Warrants or any securities convertible into, or exercisable, or exchangeable for, shares of Common
      Stock owned by it, him or her, (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any
      of the economic consequences of ownership of any Units, shares of Common Stock, Founder Shares, Warrants or any securities convertible
      into, or exercisable, or exchangeable for, shares of Common Stock owned by it, him or her, whether any such transaction is to
      be settled by delivery of such securities, in cash or otherwise, or (iii) publicly announce any intention to effect any transaction,
      including the filing of a registration statement, specified in clause (i) or (ii). The provisions of this paragraph will not apply
      (i) to the transfer of Founder Shares to any independent director appointed or elected to the Company’s board of directors
      after the Public Offering or (ii) if the release or waiver is effected solely to permit a transfer not for consideration and,
      in each case the transferee has agreed in writing to be bound by the same terms described in this Letter Agreement to the extent
      and for the duration that such terms remain in effect at the time of the transfer.

   

  4.
      In the event of the liquidation of the Trust Account upon the failure of the Company to consummate its initial Business Combination
      within the time period set forth in the Charter, the Sponsor (which for purposes of clarification shall not extend to any other
      shareholders, members or managing managers of the Sponsor) (the “Indemnitor”) agrees to indemnify and
      hold harmless the Company against any and all loss, liability, claim, damage and expense whatsoever (including, but not limited
      to, any and all legal or other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether
      pending or threatened) to which the Company may become subject as a result of any claim by (i) any third party for services rendered
      or products sold to the Company or (ii) any prospective target business with which the Company has entered into a written letter
      of intent, confidentiality or other similar agreement or Business Combination agreement (a “Target”);
      provided, however, that such indemnification of the Company by the Indemnitor (x) shall apply only to the extent necessary to
      ensure that such claims by a third party or a Target do not reduce the amount of funds in the Trust Account to below the lesser
      of (i) $10.00 per Offering Share and (ii) the actual amount per Offering Share held in the Trust Account as of the date of the
      liquidation of the Trust Account, if less than $10.00 per Offering Share is then held in the Trust Account due to reductions in
      the value of the trust assets, less taxes payable, (y) shall not apply to any claims by a third party or a Target which executed
      a waiver of any and all rights to the monies held in the Trust Account (whether or not such waiver is enforceable) and (z) shall
      not apply to any claims under the Company’s indemnity of the Underwriters against certain liabilities, including liabilities
      under the Securities Act of 1933, as amended. In the event that any such executed waiver
        by a third party or a Target is deemed to be unenforceable against such third party or Target, the Sponsor shall not be responsible
        to the extent of any liability for such third-party claims. The Indemnitor shall have the right to defend against any such
      claim with counsel of its choice reasonably satisfactory to the Company if, within 15 days following written receipt of notice
      of the claim to the Indemnitor, the Indemnitor notifies the Company in writing that it shall undertake such defense. For
        the avoidance of doubt, none of the Company’s officers or directors will indemnify the Company for claims by third parties,
        including, without limitation, claims by vendors and prospective target businesses.

   

  
     

    
      

    

  

   

   

  5.
      To the extent that the Underwriters do not exercise their over-allotment option to purchase up to an additional 3,750,000 Units
      within 45 days from the date of the Prospectus (and as further described in the Prospectus), the Sponsor agrees to forfeit, at
      no cost, a number of Founder Shares in the aggregate equal to 937,500 multiplied by a fraction, (i) the numerator of which is
      3,750,000 minus the number of Units purchased by the Underwriters upon the exercise of their over-allotment option, and (ii) the
      denominator of which is 3,750,000. The forfeiture will be adjusted to the extent that the over-allotment option is not exercised
      in full by the Underwriters so that the Founder Shares will represent an aggregate of 20.0% of the Company’s issued and
      outstanding shares of Class A Common Stock after the Public Offering (not including shares of Class A Common Stock underlying
      the Warrants or Private Placement Warrants (as defined below)). The Sponsor further agrees that to the extent that the size of
      the Public Offering is increased or decreased, the Company will purchase or sell shares or effect a share repurchase or share
      capitalization, as applicable, immediately prior to the consummation of the Public Offering in such amount as to maintain the
      ownership of the initial shareholders prior to the Public Offering at 20.0% of its issued and outstanding Capital Shares upon
      the consummation of the Public Offering. In connection with such increase or decrease in the size of the Public Offering, then
      (A) the references to 3,750,000 in the numerator and denominator of the formula in the first sentence of this paragraph shall
      be changed to a number equal to 15% of the number of Public Shares included in the Units issued in the Public Offering and (B)
      the reference to 937,500 in the formula set forth in the first sentence of this paragraph shall be adjusted to such number of
      Founder Shares that the Sponsor would have to surrender to the Company in order for the initial shareholders to hold an aggregate
      of 20.0% of the Company’s issued and outstanding shares of Class A Common Stock after the Public Offering (not including
      shares of Class A Common Stock underlying the Warrants or Private Placement Warrants).

   

  6.
      The Sponsor and each Insider hereby agrees and acknowledges that: (i) the Underwriters and the Company would be irreparably injured
      in the event of a breach by such Sponsor or an Insider of its, his or her obligations under paragraphs 1, 2, 3, 4, 5, 7(a), 7(b)
      and 9, as applicable, of this Letter Agreement (ii) monetary damages may not be an adequate remedy for such breach and (iii) the
      non-breaching party shall be entitled to injunctive relief, in addition to any other remedy that such party may have in law or
      in equity, in the event of such breach.

   

  7.
      (a) The Sponsor and each Insider agrees that it, he or she shall not Transfer any Founder Shares (or any shares of Class A Common
      Stock issuable upon conversion thereof) until the earlier of (A) one year after the completion of the Company’s initial
      Business Combination and (B) subsequent to the Business Combination, (x) if the closing price of the Class A Common Stock equals
      or exceeds $12.00 per share (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations and the like) for
      any 20 trading days within any 30-trading day period commencing at least 150 days after the Company’s initial Business Combination
      or (y) the date on which the Company completes a liquidation, merger, capital stock exchange, reorganization or other similar
      transaction that results in all of the Company’s stockholders having the right to exchange their shares of Class A Common
      Stock for cash, securities or other property (the “Founder Shares Lock-up Period”).

   

  (b)
      The Sponsor and each Insider agrees that it, he or she shall not Transfer any Private Placement Warrants (or any share of Class
      A Common Stock issued or issuable upon the exercise of the Private Placement Warrants), until 30 days after the completion of
      a Business Combination (the “Private Placement Warrants Lock-up Period”, together with the Founder Shares
      Lock-up Period, the “Lock-up Periods”).

   

  (c)
      Notwithstanding the provisions set forth in paragraphs 7(a) and (b), Transfers of the Founder Shares, Private Placement Warrants
      and shares of Class A Common Stock issued or issuable upon the exercise or conversion of the Private Placement Warrants or the
      Founder Shares that are held by the Sponsor, any Insider or any of their permitted transferees (that have complied with this paragraph
      7(c)), are permitted (i) to the Company’s officers or directors, any affiliate or family member of any of the Company’s
      officers or directors, any affiliate of the Sponsor or to any members of the Sponsor or any of their affiliates; (ii) in the case
      of an individual, by gift to a member of such individual’s immediate family or to a trust, the beneficiary of which is a
      member of such individual’s immediate family, an affiliate of such individual or to a charitable organization; (iii) in
      the case of an individual, by virtue of laws of descent and distribution upon death of such individual; (iv) in the case of an
      individual, pursuant to a qualified domestic relations order; (v) by private sales or transfers made in connection with any forward
      purchase agreement or any financing transaction or similar arrangement or in connection with the consummation of an initial Business
      Combination at prices no greater than the price at which each type of security was originally purchased; (vi) in the event of
      the Company’s liquidation prior to the completion of an initial Business Combination; (vii) by virtue of the laws of the
      State of Delaware (viii) the Amended and Restated Operating Agreement of the Sponsor, as amended, supplemented or modified, from
      time to time ; or (ix) in the event of the Company’s liquidation, merger, capital stock exchange or other similar transaction
      which results in all of the Company’s stockholders having the right to exchange their shares of Class A Common Stock for
      cash, securities or other property subsequent to the Company’s completion of an initial Business Combination; provided,
      however, that in the case of clauses (a) through (f), these permitted transferees must enter into a written agreement with the
      Company agreeing to be bound by the transfer restrictions herein and the other restrictions contained in this Agreement (including
      provisions relating to voting, the Trust Account and liquidating distributions).

   

  
     

    
      

    

  

   

  8.
      The Sponsor and each Insider represents and warrants that it, he or she has never been suspended or expelled from membership in
      any securities or commodities exchange or association or had a securities or commodities license or registration denied, suspended
      or revoked. Each Insider’s biographical information furnished to the Company (including any such information included in
      the Prospectus) is true and accurate in all respects and does not omit any material information with respect to the Insider’s
      background. The Sponsor and each Insider’s questionnaire furnished to the Company is true and accurate in all respects.
      The Sponsor and each Insider represents and warrants that: it, he or she is not subject to or a respondent in any legal action
      for, any injunction, cease-and-desist order or order or stipulation to desist or refrain from any act or practice relating to
      the offering of securities in any jurisdiction; it, he or she has never been convicted of, or pleaded guilty to, any crime (i)
      involving fraud, (ii) relating to any financial transaction or handling of funds of another person, or (iii) pertaining to any
      dealings in any securities and it, he or she is not currently a defendant in any such criminal proceeding.

   

  9.
      Except as disclosed in the Prospectus, neither the Sponsor nor any officer, nor any affiliate of the Sponsor or any officer, nor
      any director of the Company, shall receive from the Company any finder’s fee, reimbursement, consulting fee, non-cash payments,
      monies in respect of any repayment of a loan or other compensation prior to, or in connection with any services rendered in order
      to effectuate, the consummation of the Company’s initial Business Combination (regardless of the type of transaction that
      it is), other than the following, none of which will be made from the proceeds held in the Trust Account prior to the completion
      of the initial Business Combination: repayment of a loan and advances up to an aggregate of $300,000 made to the Company by the
      Sponsor to cover offering-related and organizational expenses; payment to an affiliate of the Sponsor for certain office space,
      secretarial and administrative support as may be reasonably required by the Company for a total of $20,000 per month; cash compensation
      to an affiliate of the Sponsor, for any financial advisory, placement agency or other similar investment banking services that
      such affiliate may provide to our company, in connection with our initial Business Combination, including, but not limited to,
      the Marketing Fee (as defined in the Prospectus) payable to the Representative and an affiliate of the Sponsor, upon the consummation
      of our initial business combination, and reimbursement to such affiliate for any out-of-pocket expenses incurred by it in connection
      with the performance of such services; reimbursement for any reasonable out-of-pocket expenses related to identifying, investigating,
      negotiating and consummating an initial Business Combination, and repayment of non-interest bearing loans which may be made by
      the Sponsor or an affiliate of the Sponsor or certain of the Company’s officers and directors to finance transaction costs
      in connection with an intended initial Business Combination, provided, that, if the Company does not consummate an initial Business
      Combination, a portion of the working capital held outside the Trust Account may be used by the Company to repay such loaned amounts
      so long as no proceeds from the Trust Account are used for such repayment. Up to $1,500,000 of such loans may be convertible into
      warrants of the post-business combination entity at a price of $1.00 per warrant at the option of the lender Such warrants would
      be identical to the Private Placement Warrants (as defined below), including as to exercise price, exercisability and exercise
      period.

   

  10.
      The Sponsor and each Insider has full right and power, without violating any agreement to which it is bound (including, without
      limitation, any non-competition or non-solicitation agreement with any employer or former employer), to enter into this Letter
      Agreement and, as applicable, to serve as an officer and/or director on the board of directors of the Company and hereby consents
      to being named in the Prospectus as an officer and/or director of the Company.

   

  
     

    
      

    

  

   

  11.
      As used herein, (i) “Business Combination” shall mean a merger, capital stock exchange, asset acquisition,
      stock purchase, reorganization or similar business combination, involving the Company and one or more businesses; (ii) “Common
          Stock” shall mean the Class A common stock and Class B common stock, par value $0.0001 per share (“Class
          B Common Stock”); (iii) “Founder Shares” shall mean the 7,187,500 shares of Class B common
      stock issued and outstanding (up to 937,500 Shares of which are subject to complete or partial forfeiture if the over-allotment
      option is not exercised by the Underwriters); (iv) “Initial Stockholders” shall mean the Sponsor and
      any Insider that holds Founder Shares; (v) “Private Placement Warrants” shall mean the 8,250,000 Warrants
      that the Sponsor has agreed to purchase for an aggregate purchase price of $8,250,000, or $1.00 per Warrant, in a private placement
      that shall occur simultaneously with the consummation of the Public Offering; (vi) “Public Stockholders”
      shall mean the holders of securities issued in the Public Offering; (vii) “Trust Account” shall mean
      the trust fund into which a portion of the net proceeds of the Public Offering and the sale of the Private Placement Warrants
      shall be deposited; (viii) “Transfer” shall mean the (a) sale of, offer to sell, contract or agreement
      to sell, hypothecate, pledge, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly or
      indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call equivalent
      position within the meaning of Section 16 of the Exchange Act, and the rules and regulations of the Commission promulgated thereunder
      with respect to, any security, (b) entry into any swap or other arrangement that transfers to another, in whole or in part, any
      of the economic consequences of ownership of any security, whether any such transaction is to be settled by delivery of such securities,
      in cash or otherwise, or (c) public announcement of any intention to effect any transaction specified in clause (a) or (b); and
      (ix) “Warrants” shall mean the Private Placement Warrants and public warrants.

   

  12.
      The Company will maintain an insurance policy or policies providing directors’ and officers’ liability insurance,
      and each Director shall be covered by such policy or policies, in accordance with its or their terms, to the maximum extent of
      the coverage available for any of the Company’s directors or officers.

   

  13.
      This Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter
      hereof and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral,
      to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement
      may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision,
      except by a written instrument executed by all parties hereto.

   

  14.
      No party hereto may assign either this Letter Agreement or any of its rights, interests, or obligations hereunder without the
      prior written consent of the other parties. Any purported assignment in violation of this paragraph shall be void and ineffectual
      and shall not operate to transfer or assign any interest or title to the purported assignee. This Letter Agreement shall be binding
      on the Sponsor and each Insider and their respective successors, heirs and assigns and permitted transferees.

   

  15.
      Nothing in this Letter Agreement shall be construed to confer upon, or give to, any person or corporation other than the parties
      hereto any right, remedy or claim under or by reason of this Letter Agreement or of any covenant, condition, stipulation, promise
      or agreement hereof. All covenants, conditions, stipulations, promises and agreements contained in this Letter Agreement shall
      be for the sole and exclusive benefit of the parties hereto and their successors, heirs, personal representatives and assigns
      and permitted transferees.

   

  16.
      This Letter Agreement may be executed in any number of original or facsimile counterparts and each of such counterparts shall
      for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

   

  17.
      This Letter Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall
      not affect the validity or enforceability of this Letter Agreement or of any other term or provision hereof. Furthermore, in lieu
      of any such invalid or unenforceable term or provision, the parties hereto intend that there shall be added as a part of this
      Letter Agreement a provision as similar in terms to such invalid or unenforceable provision as may be possible and be valid and
      enforceable.

   

  
     

    
      

    

  

   

  18.
      This Letter Agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York without
      giving effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction.
      The parties hereto (i) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this
      Letter Agreement shall be brought and enforced in the courts of New York City, in the State of New York, and irrevocably submit
      to such jurisdiction and venue, which jurisdiction and venue shall be exclusive and (ii) waive any objection to such exclusive
      jurisdiction and venue or that such courts represent an inconvenient forum.

   

  19.
      Any notice, consent or request to be given in connection with any of the terms or provisions of this Letter Agreement shall be
      in writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt requested),
      by hand delivery or facsimile transmission.

   

  20.
      This Letter Agreement shall terminate on the earlier of (i) the expiration of the Lock-up Periods or (ii) the liquidation of the
      Company; provided, however, that this Letter Agreement shall earlier terminate in the event that the Public Offering is not consummated
      by July 31, 2021; provided further that paragraph 4 of this Letter Agreement shall survive such liquidation.

   

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  	 	Sincerely,
	 	 	 
	 	ARROWROOT ACQUISITION LLC
	 	 	 
	 	By:	 /s/ Matthew Safaii
	 	 	Name: Matthew Safaii
	 	 	Title:   Principal
	 	 	 
	 	By:	 /s/ Thomas Olivier
	 	 	Name: Thomas Olivier
	 	 	 
	 	By:	 /s/ Gaurav Dhillon
	 	 	Name: Gaurav Dhillon
	 	 	 
	 	By:	 /s/ Dixon Doll
	 	 	Name: Dixon Doll
	 	 	 
	 	By:	 /s/ Will Semple
	 	 	Name: Will Semple
	 	 	 
	 	By:	 /s/ Matthew Safaii
	 	 	Name: Matthew Safaii


  	 	 


  	Acknowledged and Agreed:	 
	 	 
	ARROWROOT ACQUISITION CORP.	 
	 	 	 
	By:	 /s/ Matthew Safaii	 
	 	Name: Matthew Safaii	 
	 	Title:   Chief Executive Officer 	 


   

  [Signature
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