Question

In the following exercises, simplify.

$\sqrt{\frac{28q^6}{225}}$

Short answer

The required answer is$\frac{2q^3\sqrt{7}}{15}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

${\sqrt{\frac{28q^6}{225}}}_{}$

Step 2. Use the quotient property to simplify the square root.

$\sqrt{\frac{28q^6}{225}}$

Rewrite using the quotient property,

$\frac{\sqrt{28q^6}}{\sqrt{225}}$

Simplify the radicals in the numerator and the denominator,

$\frac{\sqrt{4q^6}·\sqrt{7}}{\sqrt{225}}$

Simplify,

$\frac{2q^3\sqrt{7}}{15}$