# How do you simplify sqrt((3x^3)/(64x^2))?

Apr 5, 2017

$\frac{\sqrt{3 x}}{8}$

#### Explanation:

Remember that if you dividing under a root, you can split it into two separate roots:

sqrt((3x^3)/(64x^2)) = (sqrt(3x^3))/(sqrt(64x^2)) = (sqrt(3x xx x^2))/(sqrt(64x^2)

Now find the square roots where you can:

$\frac{\sqrt{3 x \times \textcolor{red}{{x}^{2}}}}{\sqrt{\textcolor{b l u e}{64 {x}^{2}}}} = \frac{\textcolor{red}{x} \sqrt{3 x}}{\textcolor{b l u e}{8 x}}$

Now simplify:

$\frac{\sqrt{3 x}}{8}$

OR you could simplify under the root first:

$\sqrt{\frac{3 {x}^{3}}{64 {x}^{2}}} = \sqrt{\frac{3 x}{64}}$

$= \frac{\sqrt{3 x}}{8}$