Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4: 19

Answer

$24 \sqrt{5}$

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 8. Also, recall, $\sqrt{a}\times \sqrt{b}= \sqrt{a \times b}$. Thus, we can multiply 3 and 15 to obtain the simplified expression: $8\sqrt{3 \times 15}=8\sqrt{45}$ 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 9 and 5 are factors of 45. We know that 9 is a perfect square, so we simplify: $8 \sqrt{9} \sqrt{5}=24 \sqrt{5}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.