# Chapter 10 - Exponents and Radicals - Review Exercises: Chapter 10 - Page 693: 34

$15\sqrt{2}$

#### Work Step by Step

Extracting the factors that are perfect powers of the index, the given expression simplifies to \begin{array}{l}\require{cancel} \sqrt{50}+2\sqrt{18}+\sqrt{32} \\\\= \sqrt{25\cdot2}+2\sqrt{9\cdot2}+\sqrt{16\cdot2} \\\\= \sqrt{(5)^2\cdot2}+2\sqrt{(3)^2\cdot2}+\sqrt{(4)^2\cdot2} \\\\= 5\sqrt{2}+2\cdot3\sqrt{2}+4\sqrt{2} \\\\= 5\sqrt{2}+6\sqrt{2}+4\sqrt{2} \\\\= (5+6+4)\sqrt{2} \\\\= 15\sqrt{2} .\end{array}

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