## Elementary Algebra

Published by Cengage Learning

# Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3: 56

#### Answer

$\dfrac{5\sqrt{y}}{y^3}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\sqrt{\dfrac{25}{y^5}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{25}{y^4}\cdot\dfrac{1}{y}} \\\\= \sqrt{\left( \dfrac{5}{y^2}\right)^2\cdot\dfrac{1}{y}} \\\\= \dfrac{5}{y^2}\sqrt{\dfrac{1}{y}} \\\\= \dfrac{5}{y^2}\sqrt{\dfrac{1}{y}\cdot\dfrac{y}{y}} \\\\= \dfrac{5}{y^2}\sqrt{\dfrac{y}{y^2}} \\\\= \dfrac{5}{y^2}\cdot\dfrac{\sqrt{y}}{\sqrt{y^2}} \\\\= \dfrac{5}{y^2}\cdot\dfrac{\sqrt{y}}{y} \\\\= \dfrac{5\sqrt{y}}{y^3} .\end{array} Note that all variables are assumed to represent positive real numbers.

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