# How do you simplify 14sqrt20 - 3sqrt125?

Jul 2, 2016

$14 \sqrt{20} - 3 \sqrt{125} = 13 \sqrt{5}$

#### Explanation:

$14 \sqrt{20} - 3 \sqrt{125}$

= $14 \sqrt{2 \times 2 \times 5} - 3 \sqrt{5 \times 5 \times 5}$

= $14 \sqrt{\underline{2 \times 2} \times 5} - 3 \sqrt{\underline{5 \times 5} \times 5}$

= $14 \times 2 \times \sqrt{5} - 3 \times 5 \times \sqrt{5}$

= $28 \sqrt{5} - 15 \sqrt{5}$

= $\left(28 - 15\right) \sqrt{5}$

= $13 \sqrt{5}$

Jul 2, 2016

$14 \sqrt{20} - 3 \sqrt{125} = 13 \sqrt{5}$

#### Explanation:

Note that if $a , b \ge 0$ then:

$\sqrt{a b} = \sqrt{a} \sqrt{b}$

In particular:

$\sqrt{{a}^{2} b} = \sqrt{{a}^{2}} \sqrt{b} = a \sqrt{b}$

So we can move square factors outside the square root like this:

$14 \sqrt{20} - 3 \sqrt{125}$

$= 14 \sqrt{{2}^{2} \cdot 5} - 3 \sqrt{{5}^{2} \cdot 5}$

$= 14 \sqrt{{2}^{2}} \sqrt{5} - 3 \sqrt{{5}^{2}} \sqrt{5}$

$= \left(14 \cdot 2 \cdot \sqrt{5}\right) - \left(3 \cdot 5 \cdot \sqrt{5}\right)$

$= 28 \sqrt{5} - 15 \sqrt{5}$

$= \left(28 - 15\right) \sqrt{5}$

$= 13 \sqrt{5}$