## Intermediate Algebra for College Students (7th Edition)

Published by Pearson

# Chapter 7 - Section 7.3 - Multiplying and Simplifying Radical Expressions - Exercise Set - Page 531: 74

#### Answer

$2x^5 \sqrt {6x}$

#### Work Step by Step

Apply product rule: $\sqrt[n] p \sqrt[n] q=\sqrt[n]{pq}$ Here, $n$ refers as index. $\sqrt {2x^7} \sqrt {12x^4}=\sqrt {(2x^7) (12x^4)}= \sqrt{24 x^{11}}$ The radical $\sqrt{24 x^{11}}$ can be further simplified by using product rule again. Such as: $\sqrt{24 x^{11}}=\sqrt {(4x^{10}) (6x)}=\sqrt {(2x^5)^2 (6x)}=2x^5 \sqrt {6x}$

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