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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 9.130. (page 1083)

Simplify: $\frac{\sqrt{300 m^{3} n^{7}}}{\sqrt{3 m^{5} n}}$ .

Short Answer

Expert verified

Simplified form of $\frac{\sqrt{300 m^{3} n^{7}}}{\sqrt{3 m^{5} n}}$ is $\frac{10 n^{3}}{m}$ .

Step by step solution

01

Step 1. Given information.

Given a fraction $\frac{\sqrt{300 m^{3} n^{7}}}{\sqrt{3 m^{5} n}}$ .

02

Step 2. Rewrite using the quotient property of square roots.

Quotient property of square roots says that if a, b are non-negative number and $b 鈮� 0$ , then $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ .

It follows that $\frac{\sqrt{300 m^{3} n^{7}}}{\sqrt{3 m^{5} n}} = \sqrt{\frac{300 m^{3} n^{7}}{3 m^{5} n}}$ .

03

Step 3. Remove common factors.

Remove common factor as follows.

$\begin{array}{rcl} \sqrt{\frac{300 m^{3} n^{7}}{3 m^{5} n}} & = & \sqrt{\frac{3 路 100 路 m^{3} 路 n 路 n^{6}}{3 路 m^{3} 路 m^{2} 路 n}} \\ = & \sqrt{\frac{100 n^{6}}{m^{2}}} \end{array}$

04

Step 4. Simplify the radical.

Simplify the radical as follows.

$\begin{array}{rcl} \sqrt{\frac{100 n^{6}}{m^{2}}} & = & \sqrt{\frac{{(10 n^{3})}^{2}}{m^{2}}} \\ = & \frac{10 n^{3}}{m} \end{array}$

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Most popular questions from this chapter

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