Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 8 - Review Exercises - Page 619: 15


$$4x\sqrt 3x$$

Work Step by Step

We can use the product rule for square roots to rewrite the radicand as a product of the greatest perfect square factor and another factor. We can see that the radicand $48x^3$ can be broken down into two factors: the perfect square $16x^2$ and $3x$: $$(\sqrt 16x^2)(\sqrt 3x)$$ Because $16x^2$ is a perfect square, we go ahead and simplify the expression by taking the square root of $16x^2$, which is $4x$: $$4x\sqrt 3x$$
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