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 7.4 - Adding, Subtracting, and Dividing Radical Expressions - Exercise Set - Page 539: 67

Answer

$ \frac{43\sqrt {2}}{35} $.

Work Step by Step

The given expression is $=\frac{\sqrt {32}}{5}+\frac{\sqrt {18}}{7}$ Factor the radicands into square terms. $=\frac{\sqrt {4^2\cdot 2}}{5}+\frac{\sqrt {3^2\cdot 2}}{7}$ Simplify. $=\frac{4\sqrt {2}}{5}+\frac{3\sqrt { 2}}{7}$ Using the distributive property: $=\sqrt {2} \left ( \frac{4}{5}+\frac{3}{7} \right )$ Multiply and divide the first fraction by $7$ and the second by $5$ $=\sqrt {2} \left ( \frac{7\cdot 4}{7\cdot 5}+\frac{5\cdot 3}{5\cdot 7} \right )$ $=\sqrt {2} \left ( \frac{28}{35}+\frac{15}{35} \right )$ $=\sqrt {2} \left ( \frac{28+15}{35} \right )$ Simplify. $=\sqrt {2} \left ( \frac{43}{35} \right )$ Clear the parentheses. $= \frac{43\sqrt {2}}{35} $.
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