# How do you simplify sqrt75+sqrt3?

Oct 9, 2015

$6 \sqrt{3}$

#### Explanation:

Notice that you can write

$75 = 25 \cdot 3 = 5 \cdot 5 \cdot 3 = {5}^{2} \cdot 3$

This means that the expression can be written as

$\sqrt{75} + \sqrt{3} = \sqrt{{5}^{2} \cdot 3} + \sqrt{3}$

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

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

$= \sqrt{3} \cdot \left(5 + 1\right)$

$= \textcolor{g r e e n}{6 \sqrt{3}}$