質問: What is the square root of 8 divided by square root of 5 minus square root of 2? ================================================================================
回答: #(2sqrt10+4)/3# #### Explanation: #sqrt8/(sqrt 5-sqrt 2)# #:.(sqrt 5+sqrt 2)/(sqrt 5+sqrt 2)=1# #:.=sqrt8/(sqrt 5-sqrt 2)xx (sqrt 5+sqrt 2)/(sqrt 5+sqrt 2)# #(sqrt8(sqrt5+sqrt2))/((sqrt5-sqrt2)(sqrt5+sqrt2))# #:.=(sqrt 8(sqrt 5+sqrt 2))/3# #:.=(sqrt 8 sqrt 5+sqrt 8 sqrt 2)/3# #:.=(sqrt(8*5)+sqrt(8*2))/3# #:.=(sqrt 40+sqrt 16)/3# #:.=(sqrt(2*2*2*5)+sqrt 16)/3# #:.=sqrt2*sqrt2=2# #:.=(sqrt(2*2*2*5)+4)/3# #:.=(2 sqrt (2*5)+4)/3# #:.=(2 sqrt10+4)/3#