Question

What is the simplified form of square root of 10 - square root of 5 over square root of 10 + square root of 5?

Answer 1

`(sqrt(10)-sqrt(5))/(sqrt(10)+sqrt(5)=3-2sqrt(2)`

Explanation:

`(sqrt(10)-sqrt(5))/(sqrt(10)+sqrt(5)`
`color(white)("XXX")=cancel(sqrt(5))/cancel(sqrt(5))*(sqrt(2)-1)/(sqrt(2)+1)`

`color(white)("XXX")=(sqrt(2)-1)/(sqrt(2)+1)*(sqrt(2)-1)/(sqrt(2)-1)`

`color(white)("XXX")=(sqrt(2)-1)^2/((sqrt(2)^2-1^2)`

`color(white)("XXX")=(2-2sqrt2+1)/(2-1)`

`color(white)("XXX")=3-2sqrt(2)`