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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.43 (page 766)

Simplify: $\sqrt{\frac{24 p^{3}}{49}} .$

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information

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

We have to simplify it.

02

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

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

03

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

After simplifying we get,

$\frac{\sqrt{24 p^{3}}}{\sqrt{49}} = \frac{\sqrt{{(2 p)}^{2}} 路 \sqrt{6 p}}{\sqrt{{(7)}^{2}}} = \frac{2 p \sqrt{6 p}}{7}$

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Most popular questions from this chapter

Explain why $7 + \sqrt{9}$ is not equal to $\sqrt{7 + 9}$ .

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{80 q^{5}}}{\sqrt{5 q}}$

(b) $\frac{\sqrt[3]{- 625}}{\sqrt[3]{5}}$

(c) $\frac{\sqrt[4]{80 m^{7}}}{\sqrt[4]{5 m}}$

In the following exercises, solve.

$\sqrt{5 x - 6} = 8$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{192 q^{3} r^{7}}, \sqrt[3]{54 m^{9} n^{10}}, \sqrt[4]{81 a^{9} b^{8}}$

In the following exercises, solve.

$\sqrt{2 m - 3} - 5 = 0$

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