Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - Chapter Review - Page 423: 9

Answer

$$9|x|$$

Work Step by Step

RECALL: (1) For any real numbers $a \ge 0, b\ge0$, $\sqrt{ab}=\sqrt{a} \cdot \sqrt{b}$. (2) For any real numbers $a \ge 0, b\gt 0$, $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$. (3) $\sqrt{a^2}=|a|$ Use rule (1) above to obtain: \begin{align*} \sqrt{81x^2}&=\sqrt{81}\cdot \sqrt{x^2}\\ &=9\sqrt{x^2} \end{align*} Use rule (3) above to obtain: \begin{align*} 9\sqrt{x^2}&=9 \cdot |x|\\ &=9|x| \end{align*}
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