Chapter 9: Q 139. (page 1054)

In the following exercises, simplify.
$\sqrt{\frac{27 p^{2} q}{108 p^{5} q^{3}}}$

Short Answer

Expert verified

The required answer is $\frac{1}{2 p q \sqrt{p}}$ .

Step by step solution

Step 1. Given information.

The given expression is:

$\sqrt{\frac{27 p^{2} q}{108 p^{5} q^{3}}}$

Step 2. Use the quotient property to simplify the square root.

$\sqrt{\frac{27 p^{2} q}{108 p^{5} q^{3}}}$

Simplify the fraction inside the radical first. Rewrite showing common factors,

\sqrt{\frac{27 p^{2} q}{27 \cdot 4 \cdot p^{5} q^{3}}}

Simplify the fraction by removing common factors,

\sqrt{\frac{1}{4 p^{3} q^{2}}}

Rewrite using the quotient property,

role="math" localid="1648295546696" $\frac{\sqrt{1}}{\sqrt{4 p^{3} q^{2}}} = \frac{\sqrt{1}}{\sqrt{4 p^{2} q^{2}} \cdot \sqrt{p}}$

Simplify,

$\frac{1}{2 p q \sqrt{p}}$

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In the following exercises, simplify.
$\sqrt{\frac{27 p^{2} q}{108 p^{5} q^{3}}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use the quotient property to simplify the square root.

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In the following exercises, simplify.27p2q108p5q3

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use the quotient property to simplify the square root.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Decision Maths

Logic and Functions

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
$\sqrt{\frac{27 p^{2} q}{108 p^{5} q^{3}}}$