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: 18

Answer

$9a \sqrt {2}$

Work Step by Step

We first separate the number and the variable into two separate square roots: $ 3\sqrt {18} \times \sqrt {a^{2}} = 3 \sqrt {18} \times a$ 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 18 has factors of 2 and 9. 9 is a perfect square, so we know that we can simplify: $3a\sqrt {18} = 3a \times \sqrt {9} \times \sqrt {2} = 9a \sqrt {2}$
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