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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-\sqrt{-72}$

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Introduction to complex numbers

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Q. Use the imaginary number

i

to rewrite the expression below as a complex number. Simplify all radicals.

-\sqrt{-72}

Break down expression: First, let's break $-\sqrt{-72}$ into $-\sqrt{-1 \times 72}$ .
Use imaginary unit: Now, we know that $\sqrt{-1}$ is the imaginary unit $i$ , so we can write $-\sqrt{-72}$ as $-i \times \sqrt{72}$ .
Factorize $72$ : Next, we simplify $\sqrt{72}$ . The number $72$ can be factored into $36 \times 2$ , where $36$ is a perfect square.
Simplify radical: So, $\sqrt{72}$ is the same as $\sqrt{36 \times 2}$ , which simplifies to $\sqrt{36} \times \sqrt{2}$ or $6 \times \sqrt{2}$ .
Combine terms: Now we can combine the $i$ and the simplified radical to get $-i \times 6 \times \sqrt{2}$ .
Multiply to get result: Finally, we multiply $-i$ by $6 \times \sqrt{2}$ to get the complex number $-6i \times \sqrt{2}$ .

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