# How do you simplify [sqrt 18] - 2[sqrt 2]?

May 9, 2016

$\sqrt{18} - 2 \sqrt{2} = \sqrt{2}$

#### Explanation:

We will make use of the fact that $\sqrt{a b} = \sqrt{a} \cdot \sqrt{b}$ when $a$ and $b$ are positive.

From this, we can see that $\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3 \cdot \sqrt{2} = 3 \sqrt{2}$.

Thus, $\sqrt{18} - 2 \sqrt{2} = 3 \sqrt{2} - 2 \sqrt{2} = \sqrt{2} \left(3 - 2\right) = \sqrt{2} \left(1\right) = \sqrt{2}$.

May 9, 2016

$\sqrt{18} - 2 \sqrt{2} = \textcolor{b l u e}{\sqrt{2}}$

#### Explanation:

$\sqrt{18} - 2 \sqrt{2}$

Simplify $\sqrt{18}$ by writing its prime factors.

$\sqrt{2 \times 3 \times 3} - 2 \sqrt{2}$

$\sqrt{2 \times {3}^{2}} - 2 \sqrt{2}$

Apply the square root rule $\sqrt{{a}^{2}} = a$.

$3 \sqrt{2} - 2 \sqrt{2}$

Simplify.

$\sqrt{2}$