## Elementary Algebra

Published by Cengage Learning

# Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 20

#### Answer

$98 \sqrt{2}$

#### 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 14. Also, recall, $\sqrt{a}\times \sqrt{b}= \sqrt{a \times b}$. Thus, we can multiply 7 and 14 to obtain the simplified expression: $14 \sqrt{7 \times 14}=14\sqrt{98}$ 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 49 and 2 are factors of 98. We know that 49 is a perfect square, so we simplify: $14 \sqrt{49} \sqrt{2}=98 \sqrt{2}$

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