# How do you simplify sqrt 7 - 2sqrt63?

Apr 11, 2016

$- 5 \sqrt{7}$

#### Explanation:

Recall that: $\sqrt{m n} = \sqrt{m} \cdot \sqrt{n}$

Using this rule, we can rewrite your problem as:

$\sqrt{7} - 2 \cdot \sqrt{9 \cdot 7}$

Simplifying this further by taking the $\sqrt{9}$ outside, we get:

$\sqrt{7} - 2 \cdot 3 \sqrt{7}$
$= \sqrt{7} - 6 \cdot \sqrt{7}$

If we consider $\sqrt{n}$ to equal $1 \cdot \sqrt{n}$ we can further simplify the equation:

$\sqrt{7} - 6 \sqrt{7}$
$= 1 \cdot \sqrt{7} - 6 \cdot \sqrt{7}$

Therefore:

$\left(1 - 6\right) \cdot \sqrt{7}$

Completely simplified:

$= - 5 \sqrt{7}$