Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-8 Complex Numbers - Practice and Problem-Solving Exercises - Page 253: 9



Work Step by Step

Using $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b},$ the given expression, $ \sqrt{-7} ,$ is equivalent to \begin{align*} & \sqrt{-1}\cdot\sqrt{7} .\end{align*} Since $i=\sqrt{-1},$ the expression above is equivalent to \begin{align*}\require{cancel} & i\cdot\sqrt{7} \\&= i\sqrt{7} .\end{align*} Hence, the simplified form of the given expression is $ i\sqrt{7} $.
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