Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 8 - Radical Functions - 8.3 Multiplying and Dividing Radicals - 8.3 Exercises - Page 643: 48


$\frac{m^{2}\sqrt 2}{5n}$

Work Step by Step

Step 1: $\sqrt \frac{6m^{7}}{75m^{3}n^{2}}$ Step 2: $\sqrt {\frac{6}{75}\times\frac{m^{7}}{m^{3}}\times\frac{1}{n^{2}}}$ Step 3: $\sqrt {\frac{2}{25}\times\frac{m^{7-3}}{1}\times\frac{1}{n^{2}}}$ Step 4: $\sqrt {\frac{2}{25}\times\frac{m^{4}}{1}\times\frac{1}{n^{2}}}$ Step 5: $\frac{\sqrt 2}{\sqrt {25}}\times\frac{\sqrt {m^{4}}}{\sqrt 1}\times\frac{\sqrt 1}{\sqrt {n^{2}}}$ Step 6: $\frac{\sqrt 2}{5}\times\frac{ m^{2}}{1}\times\frac{1}{n}$ Step 7: $\frac{m^{2}\sqrt 2}{5n}$
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