# How do you simplify sqrt(68ac^3)/sqrt(27a^2)?

Sep 21, 2017

$\frac{2 c \sqrt{51 a c}}{9 a}$

#### Explanation:

$\frac{\sqrt{68 a {c}^{3}}}{\sqrt{27 {a}^{2}}}$ can simplify to $\frac{2 c \sqrt{17 a c}}{3 a \sqrt{3}}$
Then, you multiply fraction by 1 to not change the value of the expression.
You multiply by $\frac{\sqrt{3}}{\sqrt{3}}$ which is equal to 1.
This is because you need to get rid of the root in the denominator. $\sqrt{3} \cdot \sqrt{3} = 3$

$\frac{2 c \sqrt{17 a c}}{3 a \sqrt{3}} \cdot \left(\frac{\sqrt{3}}{\sqrt{3}}\right) = \frac{2 c \sqrt{51 a c}}{3 a \sqrt{9}} = \frac{2 c \sqrt{51 a c}}{9 a}$