Question

How do you simplify `5/(8+sqrt(7))`?

Answer 1

`(40-5sqrt7)/57`

Explanation:

Original expression

`5/(8+sqrt7)`

Multiply by conjugate

`5/(8+sqrt7)*(8-sqrt7)/(8-sqrt7)`

combine

`(5*(8 - sqrt7))/((8*8)-sqrt7*sqrt7)`

Collect terms

`(40-5sqrt7)/(64-7)` `rArr` `(40-5sqrt7)/(57)`

`~~0.47`