## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

# Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 41

#### Answer

$-\sqrt{30}$

#### Work Step by Step

Using $i=\sqrt{-1},$ $i^2=-1,$ and the properties of radicals, the given expression, $\sqrt{-3}\sqrt{-10} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{-1}\sqrt{3}\cdot\sqrt{-1}\sqrt{10} \\\\= i\sqrt{3}\cdot i\sqrt{10} \\\\= i(i)\sqrt{3(10)} \\\\= i^2\sqrt{30} \\\\= (-1)\sqrt{30} \\\\= -\sqrt{30} .\end{array}

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