Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.2 - Exponents and Radicals - 1.2 Exercises - Page 23: 82

Answer

$a)$ $\dfrac{\sqrt{3st}}{3t}$ $b)$ $\dfrac{a\sqrt[3]{b^{2}}}{b}$ $c)$ $\dfrac{\sqrt[5]{c^{2}}}{c}$

Work Step by Step

$a)$ $\sqrt{\dfrac{s}{3t}}$ Rewrite as $\dfrac{\sqrt{s}}{\sqrt{3t}}$: $\sqrt{\dfrac{s}{3t}}=\dfrac{\sqrt{s}}{\sqrt{3t}}=...$ Multiply the numerator and the denominator by $\sqrt{3t}$ and simplify: $...=\dfrac{\sqrt{s}}{\sqrt{3t}}\cdot\dfrac{\sqrt{3t}}{\sqrt{3t}}=\dfrac{\sqrt{3st}}{\sqrt{(3t)^{2}}}=\dfrac{\sqrt{3st}}{3t}$ $b)$ $\dfrac{a}{\sqrt[6]{b^{2}}}$ Multiply the numerator and the denominator by $\sqrt[6]{b^{4}}$ and simplify: $\dfrac{a}{\sqrt[6]{b^{2}}}=\dfrac{a}{\sqrt[6]{b^{2}}}\cdot\dfrac{\sqrt[6]{b^{4}}}{\sqrt[6]{b^{4}}}=\dfrac{a\sqrt[6]{b^{4}}}{\sqrt[6]{b^{6}}}=\dfrac{a\sqrt[6]{b^{4}}}{b}=\dfrac{ab^{4/6}}{b}=\dfrac{ab^{2/3}}{b}=\dfrac{a\sqrt[3]{b^{2}}}{b}$ $c)$ $\dfrac{1}{c^{3/5}}$ Rewrite as $\dfrac{1}{\sqrt[5]{c^{3}}}$: $\dfrac{1}{c^{3/5}}=\dfrac{1}{\sqrt[5]{c^{3}}}=...$ Multiply the numerator and the denominator by $\sqrt[5]{c^{2}}$ and simplify: $...=\dfrac{1}{\sqrt[5]{c^{3}}}\cdot\dfrac{\sqrt[5]{c^{2}}}{\sqrt[5]{c^{2}}}=\dfrac{\sqrt[5]{c^{2}}}{\sqrt[5]{c^{5}}}=\dfrac{\sqrt[5]{c^{2}}}{c}$
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