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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $-\sqrt{-48}$

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Introduction to complex numbers

Full solution

Q. Use the imaginary number

i

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

-\sqrt{-48}

Use imaginary unit: Now, we know that $\sqrt{-1}$ is the imaginary unit $i$ . So we can write $-\sqrt{-48}$ as $-i \times \sqrt{48}$ .
Factorize $48$ : Next, we simplify $\sqrt{48}$ . The number $48$ can be factored into $16 \times 3$ , where $16$ is a perfect square.
Simplify $\sqrt{48}$ : So, $\sqrt{48}$ is the same as $\sqrt{16 \times 3}$ , which simplifies to $4 \times \sqrt{3}$ .
Combine terms: Now we can combine the $-i$ and $4 \times \sqrt{3}$ to get the final answer: $-4i \times \sqrt{3}$ .

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