Question

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

$\sqrt{\frac{108y^4}{49}}$

Short answer

The simplified expression is,$\frac{6y^2\sqrt{3}}{7}$.

Step-by-step solution

Step 1 Given expression is,

$\sqrt{\frac{108y^4}{49}}$

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

The quotient property is given by,

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

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

Step 2 Simplify the given expression.

$\sqrt{\frac{108y^4}{49}}=\sqrt{\frac{36y^4·3}{49}}$

Now use the quotient property.

$$\begin{gathered} \sqrt{\frac{108y^4}{49}}=\frac{\sqrt{36y^4·3}}{\sqrt{49}} \\ =\frac{\sqrt{{\left(6y^2\right)}^2·\sqrt{3}}}{7} \\ =\frac{6y^2·\sqrt{3}}{7} \end{gathered}$$