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 - Page 610: 27


$ 42n^{2}$

Work Step by Step

We first combine this into one square root: $ \sqrt {18n \times 98 n^{3}} =\sqrt {1764 n^{4}}$ We now separate the number and the variable into two separate square roots: $ \sqrt {1764} \times \sqrt {n^{4}} =\sqrt {1764} \times n^{2}$ 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 1764 is a perfect square, so we know that we can simplify: $\sqrt {1764} \times n^{2}= 42n^{2}$
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