Question

`(sqrt 5 - sqrt 7) (sqrt 5 - sqrt 8)` Multiply and Simplify?

Answer 1

`(sqrt5-sqrt7)(sqrt5-sqrt8)=color(blue)(5-2sqrt10-sqrt35+2sqrt14`

Explanation:

`(sqrt5-sqrt7)(sqrt5-sqrt8)`

Use the FOIL method.
https://en.wikipedia.org/wiki/FOIL_method

`(sqrt5sqrt5)-(sqrt5sqrt8)-(sqrt5sqrt7)+(sqrt7sqrt8)`

Simplify.

`5-sqrt40-sqrt35+sqrt56`

Prime factorize the radicands.

`5-sqrt(2*2*2*5)-sqrt(5*7)+sqrt(2*2*2*7)`

Simplify.

`5-2sqrt10-sqrt35+2sqrt14`