# Chapter 10 - Exponents and Radicals - Review Exercises: Chapter 10: 52

$3i\sqrt{5}$

#### Work Step by Step

Using $i=\sqrt{-1}$ and the properties of radicals, the given expression simplifies to \begin{array}{l}\require{cancel} \sqrt{-45} \\\\= \sqrt{-1}\cdot\sqrt{45} \\\\= i\sqrt{9\cdot5} \\\\= i\sqrt{(3)^2\cdot5} \\\\= 3i\sqrt{5} .\end{array}

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