# How do you simplify (9 - sqrt2) (7 + sqrt2)?

May 20, 2016

$61 + 2 \sqrt{2}$

#### Explanation:

First, to simplify this expression, you need to use the distributive property (or FOIL):
$\left(9 - \sqrt{2}\right) \left(7 + \sqrt{2}\right)$
$9 \left(7\right) + 9 \left(\sqrt{2}\right) - \sqrt{2} \left(7\right) - \sqrt{2} \left(\sqrt{2}\right)$
$63 + 9 \sqrt{2} - 7 \sqrt{2} - \sqrt{4}$

Now, you simplify:
$63 + 2 \sqrt{2} - 2$
$63 - 2 + 2 \sqrt{2}$
$61 + 2 \sqrt{2}$