Question

In the following exercises, simplify.

$\sqrt{\frac{150r^3}{256}}$

Short answer

The required answer is$\frac{5r\sqrt{6r}}{16}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\sqrt{\frac{150r^3}{256}}$

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

$\sqrt{\frac{150r^3}{256}}$

Rewrite using the quotient property,

$\frac{\sqrt{150r^3}}{\sqrt{256}}$

Simplify the radicals in the numerator and the denominator,

$\frac{\sqrt{25r^2}·\sqrt{6r}}{\sqrt{256}}$

Simplify,

$\frac{5r\sqrt{6r}}{16}$