# Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set - Page 653: 38

$\dfrac{5\sqrt[]{ab}}{3}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\dfrac{\sqrt[]{75ab}}{3\sqrt[]{3}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{3}\sqrt[]{\dfrac{75ab}{3}} \\\\= \dfrac{1}{3}\sqrt[]{25ab} \\\\= \dfrac{1}{3}\sqrt[]{25\cdot ab} \\\\= \dfrac{1}{3}\sqrt[]{(5)^2\cdot ab} \\\\= \dfrac{1}{3}\cdot5\sqrt[]{ab} \\\\= \dfrac{5\sqrt[]{ab}}{3} .\end{array} * Note that it is assumed that all variables represent positive numbers.

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