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Question

# Write the number in i-form. $\sqrt{-48}$

Solution

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$\begin{gathered} \sqrt { - 48} \\ \textcolor{#4257b2}{{\text{Rewrite the radicand}}} \\ \sqrt { - 48} = \sqrt {\left( {16} \right)\left( 3 \right)\left( { - 1} \right)} \\ \textcolor{#4257b2}{ {\text{Apply the Product Rule for Radicals }}\sqrt[n]{{uv}} = \sqrt[n]{u}\sqrt[n]{v}} \\ \sqrt {\left( {16} \right)\left( 3 \right)\left( { - 1} \right)} = \sqrt {16} \sqrt 3 \sqrt { - 1} \\ \textcolor{#4257b2}{ {\text{Simplify}}} \\ 4\sqrt 3 i \\ \end{gathered}$

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