Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4: 18

Answer

$18 \sqrt{6}$

Work Step by Step

First of all, in order to make this one large square root, we multiply the coefficients to obtain that the new coefficient is 6. Also, recall, $\sqrt{a}\times \sqrt{b}= \sqrt{a \times b}$. Thus, we can multiply 2 and 27 to obtain the simplified expression: $6\sqrt{2 \times 27}=6\sqrt{54}$ In order to simplify a radical, we consider the factors of the number inside of the radical. If any of these factors are perfect squares, meaning that their square root is a whole number, then we can simplify the radical. We know that 9 and 6 are factors of 54. We know that 9 is a perfect square, so we simplify: $6 \sqrt{9} \sqrt{6}=18 \sqrt{6}$
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