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: 22

Answer

$3x\sqrt{2x}$

Work Step by Step

RECALL: (i) For any non-negative real numbers $a$ and $b$, $\sqrt{a} \cdot \sqrt{b} =\sqrt{ab}.$ (ii) For any non-negative real number $a$, $\sqrt{a^2}=a$. Use rule (i) above to obtain: $\sqrt{6x(3x^2)} \\=\sqrt{18x^{2+1}} \\=\sqrt{18x^3}.$ Factor the radicand so that one of the factors is a perfect square to obtain $\sqrt{9x^2(2x)} \\=\sqrt{(3x)^2(2x)}.$ Use rule (ii) above where $a=3x$ to obtain $\\3x\sqrt{2x}.$
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