Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 10 - Radical Expressions and Equations - 10-2 Simplifying Radicals - Practice and Problem-Solving Exercises - Page 623: 20


$15b^{4} \sqrt {6}$

Work Step by Step

We first separate the number and the variable into two separate square roots: $ 3\sqrt {150} \times \sqrt {b^{8}} = 3 \sqrt {150} \times b^{4}$ In order to see if a radical is in simplified form, see if any of its factors are perfect squares (meaning that their square root will be an integer). We see that 150 has factors of 25 and 6. 25 is a perfect square, so we know that we can simplify: $3b^{4}\sqrt {150} = 3b^{4} \times \sqrt {25} \times \sqrt {6} = 15b^{4} \sqrt {6}$
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