Question

How do you use FOIL to multiply `(sqrt7-sqrt8)(sqrt7-sqrt8)`?

Answer 1

Using FOIL:

`(sqrt(7)-sqrt(8))(sqrt(7)-sqrt(8))`

`= 7-sqrt(7)sqrt(8)-sqrt(8)sqrt(7)+8`

`=15-4sqrt(2)sqrt(7) = 15-4sqrt(14)`

Explanation:

FOIL helps us pick pairs of terms from each binomial to multiply, before adding together to get the result:

First: `sqrt(7) * sqrt(7) = 7`
Outside: `sqrt(7) * (-sqrt(8)) = -sqrt(7) * sqrt(8)`
Inside: `(-sqrt(8)) * sqrt(7) = -sqrt(7) * sqrt(8)`
Last: `(-sqrt(8)) * (-sqrt(8)) = 8`

Added together:

`7 - 2*sqrt(7)*sqrt(8) + 8`

Now `sqrt(8) = sqrt(2^2*2) = 2*sqrt(2)`

So our expression can be simplified to:

`15-4*sqrt(7)sqrt(2) = 15-4sqrt(14)`