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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q. 333 (page 1090)

Simplify Expressions -
$\frac{\sqrt{180 p^{5} q^{2}}}{\sqrt{3 p^{3} q^{6}}}$

Short Answer

Expert verified

The simplification of Expression will be - $\frac{2 p}{q^{2}} \sqrt{15}$

Step by step solution

01

Step 1. Given Data

Expressions -

$\frac{\sqrt{180 p^{5} q^{2}}}{\sqrt{3 p^{3} q^{6}}}$

02

Step 2. To Find

Simplify The Expressions.

03

Step 3. Explanation

Expression - $\frac{\sqrt{180 p^{5} q^{2}}}{\sqrt{3 p^{3} q^{6}}}$

Neither radicand is a perfect square, so rewrite using the quotient property of square roots -

localid="1648572747746" $\frac{\sqrt{180 p^{5} q^{2}}}{\sqrt{3 p^{3} q^{6}}} \sqrt{\frac{180 p^{5} q^{2}}{3 p^{3} q^{6}}}$

04

Step 4. Calculation

Remove common factors in the numerator and denominator.

$\sqrt{\frac{180 p^{5} q^{2}}{3 p^{3} q^{6}}} \sqrt{\frac{60 脳 3 脳 p^{3} 脳 p^{2} 脳 q^{2}}{3 脳 p^{3} 脳 q^{2} 脳 q^{4}}} \sqrt{\frac{60 p^{2}}{q^{4}}}$

Simplify -

$\sqrt{\frac{60 p^{2}}{q^{4}}} \frac{2 p}{q^{2}} \sqrt{15}$

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Most popular questions from this chapter

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