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

Jun 9, 2015

Using FOIL:

$\left(\sqrt{7} - \sqrt{8}\right) \left(\sqrt{7} - \sqrt{8}\right)$

$= 7 - \sqrt{7} \sqrt{8} - \sqrt{8} \sqrt{7} + 8$

$= 15 - 4 \sqrt{2} \sqrt{7} = 15 - 4 \sqrt{14}$

Explanation:

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

First: $\sqrt{7} \cdot \sqrt{7} = 7$
Outside: $\sqrt{7} \cdot \left(- \sqrt{8}\right) = - \sqrt{7} \cdot \sqrt{8}$
Inside: $\left(- \sqrt{8}\right) \cdot \sqrt{7} = - \sqrt{7} \cdot \sqrt{8}$
Last: $\left(- \sqrt{8}\right) \cdot \left(- \sqrt{8}\right) = 8$

$7 - 2 \cdot \sqrt{7} \cdot \sqrt{8} + 8$
Now $\sqrt{8} = \sqrt{{2}^{2} \cdot 2} = 2 \cdot \sqrt{2}$
$15 - 4 \cdot \sqrt{7} \sqrt{2} = 15 - 4 \sqrt{14}$