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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-\sqrt{-27}$

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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{-27}

Express as Product: Express $-\sqrt{-27}$ as the product of square roots and $\sqrt{-1}$ . $-\sqrt{-27} = -\sqrt{-1 \times 27}$
Recognize Imaginary Unit: Recognize that $\sqrt{-1}$ is the imaginary unit $i$ . $-\sqrt{-27} = -i \times \sqrt{27}$
Simplify Prime Factors: Simplify $\sqrt{27}$ by finding the prime factors of $27$ . $\newline$ $27 = 3 \times 3 \times 3$
Express as Multiplication: Express $\sqrt{27}$ as $\sqrt{3 \times 3 \times 3}$ .
$-i \times \sqrt{27} = -i \times \sqrt{3 \times 3 \times 3}$
Take Out Square Root: Take out the square root of $9$ (which is $3$ ) from under the radical. $\newline$ $-i \sqrt{3 \times 3 \times 3} = -i \times 3 \sqrt{3}$
Multiply by $-3i$ : Multiply $-i$ by $3$ . $-i \times 3 \times \sqrt{3} = -3i \times \sqrt{3}$

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