Question

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{180s^{10}}{144}}$

Short answer

The simplified form is $\frac{6\left|s^5\right|\sqrt{5}}{12}$.

Step-by-step solution

Step 1. Given information.

The radical expression as:

$\sqrt{\frac{180s^{10}}{144}}$.

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.

$$\begin{gathered} \sqrt{\frac{180s^{10}}{144}}=\sqrt{\frac{36s^{10}·5}{144}} \\ =\frac{\sqrt{36s^{10}·5}}{\sqrt{144}} \\ =\frac{{\sqrt{(6s^5})}^2·\sqrt{5}}{12} \\ =\frac{6{\left|s\right|}^2\sqrt{5}}{12} \end{gathered}$$