Elementary Algebra

Published by Cengage Learning

Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3: 47

Answer

$\dfrac{2\sqrt{3}}{x}$

Work Step by Step

Using the properties of radicals, the given expression, $\sqrt{\dfrac{12}{x^2}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{4}{x^2}\cdot3} \\\\= \sqrt{\left(\dfrac{2}{x}\right)^2\cdot3} \\\\= \dfrac{2}{x}\sqrt{3} \\\\= \dfrac{2\sqrt{3}}{x} .\end{array} Note that all variables are assumed to represent positive real numbers.

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