# How do you simplify square root of 8 - the square root of 66?

Jul 16, 2015

$\sqrt{8} - \sqrt{66} = \left(2 - \sqrt{33}\right) \sqrt{2}$

#### Explanation:

The $\sqrt{8}$ can be simplified as follows:

$8$ can be factored to $8 = 4 \cdot 2$

So, $\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2 \sqrt{2}$

The $\sqrt{66}$ can be factored as follows:

$\sqrt{66} = \sqrt{33 \cdot 2} = \sqrt{33} \cdot \sqrt{2}$

So,

$\sqrt{8} - \sqrt{66} = 2 \sqrt{2} - \sqrt{33} \cdot \sqrt{2}$

Factoring out the $\sqrt{2}$ we get:

$2 \sqrt{2} - \sqrt{33} \cdot \sqrt{2} = \left(2 - \sqrt{33}\right) \sqrt{2}$

Recall: $b \sqrt{a} - c \sqrt{a} = \left(b - c\right) \sqrt{a}$