Question

Use the Quotient Property to simplify square roots.

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

Short answer

The simplified form is $\frac{5\left|r\right|\sqrt{6r}}{16}$.

Step-by-step solution

Step 1. Given information.

The radical expression as:

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

Step 2. Write the concept.

To determine a simplified form of a radical expression following formula is used:

$$\begin{gathered} \sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}and \\ \frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}} \end{gathered}$$

If$\sqrt[n]{a}and\sqrt[n]{b}$are real numbers, $b\ne 0$for any integer $n\ge 2$.

Step 3. Calculation.

Simplifying the expression.

$$\begin{gathered} \sqrt{\frac{150r^3}{256}}=\sqrt{\frac{25r^2.6r}{256}} \\ =\frac{\sqrt{25r^2.6r}}{\sqrt{256}} \\ =\frac{\sqrt{{\left(5r\right)}^2}\sqrt{6r}}{16} \\ =\frac{5\left|r\right|\sqrt{6r}}{16} \end{gathered}$$