Question

In the following exercises, use the Quotient Property to simplify square roots.

$\sqrt{\frac{96x^7}{121}}$

Short answer

The simplified expression is, $\frac{4\left|x^3\right|\sqrt{6x}}{11}$.

Step-by-step solution

Step 1 Given expression is,

$\sqrt{\frac{96x^7}{121}}$.

The objective is, we need to simplify the given expression.

The quotient property is,

$\frac{a^m}{a^n}=a^{m-n}$

Also we know that,$\sqrt[n]{a^n}=\left|a\right|$.

Step 2 Simplify the given expression.

$$\begin{gathered} \sqrt{\frac{96x^7}{121}}=\sqrt{\frac{24\times 4\times x^6\times x}{11\times 11}} \\ =\sqrt{\frac{6x\times {\left(4\right)}^2{x}^6}{{\left(11\right)}^2}} \end{gathered}$$

Now use the quotient property.

role="math" localid="1644821884956" $$\begin{gathered} \sqrt{\frac{96x^7}{121}}=\frac{\sqrt{6x\times {\left(4\right)}^2{x}^6}}{\sqrt{{\left(11\right)}^2}} \\ =\frac{\sqrt{6x}.4\left|x^3\right|}{11} \end{gathered}$$