Precalculus (6th Edition)

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

Chapter R - Review of Basic Concepts - R.7 Radical Expressions - R.7 Exercises: 66

Answer

$\color{blue}{\dfrac{gh^2\sqrt{ghr}}{r^2}}$

Work Step by Step

Rationalize the denominator by multiplying $r$ to both the numerator and denominator of the radicand to obtain: $=\sqrt{\dfrac{g^3h^5(r)}{r^3(r)}} \\=\sqrt{\dfrac{g^3h^5(r)}{r^4}} \\=\sqrt{\dfrac{g^3h^5(r)}{(r^2)^2}}$ Bring out the square root of the denominator to obtain: $\\=\dfrac{\sqrt{g^3h^5r}}{r^2}$ Factor the radicand such that at least one factor is a perfect square to obtain: $\\=\dfrac{\sqrt{(g^2h^4)(ghr)}}{r^2} \\=\dfrac{\sqrt{(gh^2)^2(ghr)}}{r^2}$ Bring out the square root of the perfect square factor/s of the numerator to obtain: $\\=\color{blue}{\dfrac{gh^2\sqrt{ghr}}{r^2}}$
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