Question

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{98r^5}{100}}$

Short answer

The simplified form is$\frac{7r^2\sqrt{2r}}{10}$.

Step-by-step solution

Step 1. Given information.

The radical expression as:

$\sqrt{\frac{98r^5}{100}}$.

Step 2. Write the concept.

To determine 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.

$$\begin{gathered} \sqrt{\frac{98r^5}{100}}=\sqrt{\frac{49r^4.2r}{100}} \\ =\frac{\sqrt{49r^4.2r}}{\sqrt{100}} \\ =\frac{\sqrt{{\left(7r^2\right)}^2.}\sqrt{2r}}{10} \\ =\frac{7\left|r^2\right|\sqrt{2r}}{10} \\ =\frac{7r^2\sqrt{2r}}{10} \end{gathered}$$