Chapter 10 - Review - Page 749: 127

$2i\sqrt{2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\sqrt{-8} ,$ use the properties of radicals and the definition of an imaginary number. $\bf{\text{Solution Details:}}$ 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{8} .\end{array} Using the definition of an imaginary number which is given by $i=\sqrt{-1},$ the expression above is equivalent to \begin{array}{l}\require{cancel} i\cdot\sqrt{8} .\end{array} Simplifying the radical by extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} i\cdot\sqrt{4\cdot2} \\\\= i\cdot\sqrt{(2)^2\cdot2} \\\\= i\cdot2\sqrt{2} \\\\= 2i\sqrt{2} .\end{array}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.