prompter: What is the square root, and how do I calculate it?

assistant: The square root of a given number returns a number that, when multiplied by itself, returns the original (given) number.
For example:
The square root of 4 is 2, since 2 * 2 = 4
The square root of 36 is 6, since 6 * 6 = 36

Taking the square root of a number is the same as raising the number to the power of 0.5, for example:
36 ^ 0.5 = 6

To calculate the square root of a number, you can use any calculator that is available to you (look for a √ button). To calculate a square root by hand, you need to start with 2 numbers, square them, and then estimate a new candidate for a square root. To understand this better, I will give an example for determining the square root of 10:
3 ^ 2 = 9
4 ^ 2 = 16
-> the square root must be somewhere between 3 and 4
3.5 ^ 2 = 12.25
3.25 ^ 2 = 10.5625
3.1 ^ 2 = 9.61
-> the square root must be between 3.1 and 3.25
...
this can go on forever, since the square root of 10 is an irrational number, which means that it has an infinite amount of digits after the comma without any pattern. Calculators will display the amount of digits they are able to calculate.

assistant: The square root of a number is a value that, when multiplied by itself, gives that number. In mathematical notation, the square root of a number "x" is denoted as √x or x^(1/2).

To calculate the square root of a number, you can use a calculator or perform the computation by hand using a variety of methods, such as the long division method, the Babylonian method, or the Newton-Raphson method. For most numbers, an approximation to the square root can be found using a calculator or by using estimation techniques.

prompter: How would you find the square root of a negative number then?

assistant: The short answer is, remove the negative sign, calculate the square root as discussed above, then put the letter "i" in front of the answer.

Here's why:
A real number, multiplied by itself, will never produce a negative number.  The minus sign always cancels out.  For example, 5^2 = 25 and (-5)^2 = 25.  So the square root of a negative number requires a non-real number.  In math, we use "i" to denote an imaginary number, which is the square root of -1.  This is convenient for our calculation because it allows us to remove the minus sign while we calculate the square root.

For example, let's say we want to calculate the square root of -x.  The following are all equivalent ways to write the same thing: 
√(-x)             // The initial question
√(-1 * x)       // Separate the negative 1
√(-1) * √x    // Represent as two separate square roots
i * √x           // Simplify i

assistant: When you take the square root of a negative number, the answer becomes what is called a 'complex number'. Simply take the square root as normal, and multiply it with the symbol `i`, which signifies the imaginary number equal to √(-1). 
For example, the √(-4) = 2i. 
Note that in engineering fields, 'i' is often replaced with 'j', but symbolizes the same thing.

assistant: Defining the square root of √-1 as i, we then have that √-n is simply i√n, where √n is computed by the usual means.

assistant: You can't find the square root of a negative number because negative numbers can't be square. In order for a number to have a square root, it must first be considered square. We then reverse this process to find the root. Since negatives cancel out, the product of a number with itself will always be positive, so the set of all numbers that you could find the square root of has no negative numbers.

assistant: The square root of a number is a value that, when multiplied by itself, produces the original number. For example, the square root of 9 is 3, since 3 x 3 = 9. To calculate the square root of a number, you can use the square root calculator, the long division method, or the prime factorization method. The square root calculator is the easiest and quickest method, as it will provide you with the exact result right away. The long division method requires more steps and is more time-consuming, but it will also provide you with the exact result. The prime factorization method requires even more steps, but it is useful if you are trying to calculate the square root of a large number.

prompter: Thank you for the information!
Can you make the explanation more concise so I can post it on twitter?

assistant: "Square root is a mathematical concept where the number that, when multiplied by itself, gives the original number. To calculate: use a calculator or the √ symbol. Example: √9 = 3 #Math #SquareRoot"

assistant: Here is the explanation condensed for twitter:
The square root of a number is a value that, when multiplied by itself, equals the original number. Example: the square root of 9 is 3 (3 x 3 = 9). The quickest way is using a calculator. The long division and prime factorization also find the exact result, but take more steps

assistant: I'm sorry. I realized that my answer above was wrong. Calculating the square root is a complex mathematical process and there are multiple ways of doing it. Therefore the answer to the question "how do I calculate the square root" isn't easy to fit into a tweet. I don't have the information about the actual character limitations of Twitter, Twitter can change this number into an arbitrary number whenever they want. However, if we reduce the content of the tweet to the answer of "What is the square root?" then the tweet could look like this:

"The #squareRoot of a #number is a value that, when multiplied by itself, produces the original number. For example, the square root of 9 is 3, since 3 x 3 = 9."