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: 79

Answer

$a)$ $\dfrac{\sqrt{6}}{6}$ $b)$ $\dfrac{\sqrt{6}}{2}$ $c)$ $\dfrac{9\sqrt[4]{8}}{2}$

Work Step by Step

$a)$ $\dfrac{1}{\sqrt{6}}$ Multiply the numerator and the denominator by $\sqrt{6}$ and simplify: $\dfrac{1}{\sqrt{6}}=\dfrac{1}{\sqrt{6}}\cdot\dfrac{\sqrt{6}}{\sqrt{6}}=\dfrac{\sqrt{6}}{\sqrt{6^{2}}}=\dfrac{\sqrt{6}}{6}$ $b)$ $\sqrt{\dfrac{3}{2}}$ Rewrite as $\dfrac{\sqrt{3}}{\sqrt{2}}$: $\sqrt{\dfrac{3}{2}}=\dfrac{\sqrt{3}}{\sqrt{2}}=...$ Multiply the numerator and the denominator by $\sqrt{2}$ and simplify: $...=\dfrac{\sqrt{3}}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{6}}{\sqrt{2^{2}}}=\dfrac{\sqrt{6}}{2}$ $c)$ $\dfrac{9}{\sqrt[4]{2}}$ Multiply the numerator and the denominator by $\sqrt[4]{2^{3}}$ and simplify: $\dfrac{9}{\sqrt[4]{2}}=\dfrac{9}{\sqrt[4]{2}}\cdot\dfrac{\sqrt[4]{2^{3}}}{\sqrt[4]{2^{3}}}=\dfrac{9\sqrt[4]{2^{3}}}{\sqrt[4]{2^{4}}}=\dfrac{9\sqrt[4]{8}}{2}$
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