Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.3 - Radicals and Rational Exponents - Exercise Set - Page 45: 32

Answer

$5x^2\sqrt{2}$

Work Step by Step

RECALL: (i) For any non-negative real numbers a and b, $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$ and $\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\dfrac{a}{b}}$. (ii) For any non-negative real number a, $\sqrt{a^2}=a$. (iii) $\dfrac{a^m}{a^n} = a^{m-n}, a\ne0$. (iv) $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$. Use rule (i) above to obtain $\require{cancel} \sqrt{\dfrac{500x^3}{10x^{-1}}} \\=\sqrt{\dfrac{\cancel{500}50x^3}{\cancel{10}x^{-1}}}.$ Use rule (iii) above to obtain $\sqrt{50x^{3-(-1)}} \\=\sqrt{50x^{3+1}} \\=\sqrt{50x^4}.$ Factor the radicand so that one factor is a perfect square to obtain $\sqrt{25x^4(2)} \\=\sqrt{(5x^2)^2(2)}.$ Use rule (iv) above to obtain $\\\sqrt{(5x^2)^2} \cdot \sqrt{2}.$ Simplify to obtain $5x^2\sqrt{2}.$
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