Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - Chapter R Test Prep - Review Exercises: 108

Answer

$\color{blue}{\dfrac{8y^4\sqrt{2m}}{m^2}}$

Work Step by Step

Rationalize the denominator by multiplying $m$ to both the numerator and the denominator of the radicand to obtain: $=\sqrt{\dfrac{2^7y^8(m)}{m^3(m)}} \\=\sqrt{\dfrac{2^7y^8m}{m^4}} \\=\sqrt{\dfrac{2^6y^8(2m)}{m^4}} \\=\sqrt{\dfrac{(2^3y^4)^2(2m)}{(m^2)^2}}$ Bring out the square root of the perfect square factors to obtain: $=\dfrac{2^3y^4\sqrt{2m}}{m^2} \\=\color{blue}{\dfrac{8y^4\sqrt{2m}}{m^2}}$
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