## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter P - Section P.3 - Radicals and Rational Exponents - Exercise Set: 15

#### Answer

$3|x|\sqrt{5}$

#### Work Step by Step

RECALL: For any non-negative real numbers $a$ and $b$, $\sqrt{ab} = \sqrt{a}\cdot \sqrt{b}$ and $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$. Factor the radicand so that one factor is a perfect square to obtain $\sqrt{9x^2 \cdot 5}$. Use the rule above to obtain $\sqrt{9x^2} \cdot \sqrt{5} \\=\sqrt{(3x)^2} \cdot \sqrt{5}$. Note that the variable $x$ represents any real number. This means that $x$ could be negative. Thus, to simplify the expression, use the rule $\sqrt{a^2}=|a|$ to obtain $|3x|\sqrt{5} \\=3|x|\sqrt{5}.$

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