Question

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

$\sqrt{\frac{300m^5}{64}}$

Short answer

The simplified expression is,$\frac{10m^2.\sqrt{3m}}{8}$.

Step-by-step solution

Step 1 Given expression is,

$\sqrt{\frac{300m^5}{64}}$

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.

$$\begin{gathered} \sqrt{\frac{300m^5}{64}}=\sqrt{\frac{100m^4\times 3m}{64}} \\ =\sqrt{\frac{{\left(10m^2\right)}^2\times 3m}{{\left(8\right)}^2}} \end{gathered}$$

Now use the quotient property.

$$\begin{gathered} \sqrt{\frac{300m^5}{64}}=\frac{\sqrt{{\left(10m^2\right)}^2\times 3m}}{\sqrt{{\left(8\right)}^2}} \\ =\frac{10m^2.\sqrt{3m}}{8} \end{gathered}$$