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

$i\sqrt{7}$

#### 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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