Q. 101 - Intermediate Algebra

Question

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{28q^6}{225}}$

Step-by-Step Solution

Answer

The simplified form is $\frac{2\left|q^3\right|\sqrt{7}}{15}$.

Step 1. Given information.

The radical expression as:

$\sqrt{\frac{28q^6}{225}}$.

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.

$$\begin{gathered} \sqrt{\frac{28q^6}{225}}=\sqrt{\frac{4q^6.7}{225}} \\ =\frac{\sqrt{4q^6.7}}{\sqrt{225}} \\ =\frac{\sqrt{{\left(2q^3\right)}^2}.\sqrt{7}}{15} \\ =\frac{2\left|q^3\right|\sqrt{7}}{15} \end{gathered}$$