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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 767 (page 1154)

In the following exercises, simplify.
$\sqrt{169 m^{4} n^{2}}$

Short Answer

Expert verified

The simplification of the given expression $\sqrt{169 m^{4} n^{2}}$ is $13 m^{2} 脳 |n|$

Step by step solution

01

Step 1. Given information

Given expression is $\sqrt{169 m^{4} n^{2}}$

02

Step 2. Simplification

$\sqrt{169 m^{4} n^{2}}$

Use the root of a product $\sqrt[n]{(a 脳 b)} = \sqrt[n]{a} 脳 \sqrt[n]{b}$ is equal to the product of roots of each factor.

role="math" localid="1650360461003" $= \sqrt{169} \sqrt{m^{4}} \sqrt{n^{2}}$

Write the numbers in exponential form

$= \sqrt{13^{2}} \sqrt{m^{4}} \sqrt{n^{2}}$

Reduce the index of the radical and exponent with $2$

$= \sqrt{13^{2}} m^{2} \sqrt{n^{2}}$

Reduce the exponent of the radical and exponent with $2$

$= \sqrt{13^{2}} m^{2} 脳 |n|$

Simplify

$= 13 m^{2} 脳 |n|$

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Most popular questions from this chapter

In the following exercises, solve.

$\sqrt{8 u + 1} + 9 = 0$

In the following exercises, solve.

(a) $\sqrt{s - 8} - s = - 8$

(b)role="math" localid="1647990991155" $\sqrt{w + 25} - w + 5 = 0$

In the following exercises, simplify and rationalize the denominator.

$- \frac{9}{2 \sqrt{3}}$

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