## College Algebra (10th Edition)

Published by Pearson

# Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 49

#### Answer

$2i$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\sqrt{-4} ,$ use the properties of radicals and the equivalence $i=\sqrt{-1}.$ $\bf{\text{Solution Details:}}$ Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel} \sqrt{-1}\cdot\sqrt{4} .\end{array} Since $i=\sqrt{-1},$ the expression above is equivalent to \begin{array}{l}\require{cancel} i\sqrt{4} .\end{array} Extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} i\sqrt{(2)^2} \\\\= i(2) \\\\= 2i .\end{array}

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