# What is the square root of 27 plus the square root of 75?

Jul 14, 2015

$\sqrt{27} + \sqrt{75} = 8 \sqrt{3}$

#### Explanation:

If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$

$\sqrt{27} + \sqrt{75}$

$= \sqrt{{3}^{2} \cdot 3} + \sqrt{{5}^{2} \cdot 3}$

$= \sqrt{{3}^{2}} \sqrt{3} + \sqrt{{5}^{2}} \sqrt{3}$

$= 3 \sqrt{3} + 5 \sqrt{3}$

$= \left(3 + 5\right) \sqrt{3}$

$= 8 \sqrt{3}$