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: 22


$$5x\sqrt 2$$

Work Step by Step

We can use the product rule for square roots to rewrite the two radicals as a single radical, a product of the two radicands: $$(\sqrt 5x)(\sqrt 10x) = \sqrt (5x\times10x)$$ We multiply the factors in the radicand to get: $$\sqrt 50x^2$$ $50x^2$ is the product of the perfect square $25x^2$ and $2$. $$\sqrt(50x^2) = \sqrt (25x^2) \sqrt 2$$ Since $25x^2$ is a perfect square, we can simplify this radical by taking the square root of $25x^2$, which is $5x$: $$5x\sqrt 2$$
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