Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.5 - Multiplying with More Than One Term and Rationalizing Denominators - Exercise Set - Page 550: 78


$\displaystyle \frac{17\sqrt{10}+34}{6}$

Work Step by Step

We lose the square roots in the denominator by applying the difference of squares formula: $(a\sqrt{x}+b\sqrt{y})(a\sqrt{x}-b\sqrt{y})=(a\sqrt{x})^{2}-(b\sqrt{y})^{2}=a^{2}x-b^{2}y$ $\displaystyle \frac{17}{\sqrt{10}-2} \displaystyle \color{red}{ \cdot\frac{\sqrt{10}+2}{\sqrt{10}+2} }\qquad$ (rationalize) $ =\displaystyle \frac{17(\sqrt{10}+2)}{(\sqrt{10})^{2}-2^{2}} =\frac{17(\sqrt{10}+2)}{10-4} =\frac{17(\sqrt{10}+2)}{6}$ = $\displaystyle \frac{17\sqrt{10}+34}{6}$
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.