# How do you simplify 4sqrt27-sqrt75?

Mar 21, 2018

4sqrt27-sqrt75=color(blue)(12sqrt3-5sqrt5

#### Explanation:

Simplify:

$4 \sqrt{27} - \sqrt{75}$

Prime factorize $\sqrt{27}$.

$4 \sqrt{{3}^{2} \times 3} - \sqrt{75}$

Apply rule: $\sqrt{{a}^{2}} = a$

$4 \times 3 \sqrt{3} - \sqrt{75}$

Simplify.

$12 \sqrt{3} - \sqrt{75}$

Prime factorize $\sqrt{75}$.

$12 \sqrt{3} - \sqrt{{5}^{2} \times 5}$

Apply rule: $\sqrt{{a}^{2}} = a$

$12 \sqrt{3} - 5 \sqrt{5}$

This is as far as we can go. Since the radicands are not the same, we can not add or subtract.