Q. 8.43 - Intermediate Algebra

Question

Simplify: $\sqrt{\frac{24p^3}{49}}.$

Step-by-Step Solution

Answer

After simplifying we get, $\frac{2p\sqrt{6p}}{7}.$

Step 1. Given Information

The given expression is $\sqrt{\frac{24p^3}{49}}.$

We have to simplify it.

Step 2. Use the Quotient property to rewrite the radical as the quotient of two radicals

Thus, we write $\sqrt{\frac{24p^3}{49}}$ as $\frac{\sqrt{24p^3}}{\sqrt{49}}.$

Step 3. Simplify the radicals of both the numerator and denominator

After simplifying we get,

$$\begin{gathered} \frac{\sqrt{24p^3}}{\sqrt{49}} \\ =\frac{\sqrt{{\left(2p\right)}^2}·\sqrt{6p}}{\sqrt{{\left(7\right)}^2}} \\ =\frac{2p\sqrt{6p}}{7} \end{gathered}$$