Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

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$ We see if any of the factors of a radical are perfect squares (meaning that their square root will be an integer) to see if the radical is in its most simplified form. We see that 18 has factors of 2 and 9. 9 is a perfect square, so we know that we can simplify: $3a\sqrt {18} = a \times \sqrt {9} \times \sqrt {2} = 9a \sqrt {2}$
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