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Use the imaginary number $i$ to rewrite the expression below as a complex number. Simplify all radicals. $\sqrt{-66}$

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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{-66}

Express as Product: First, let's express $\sqrt{-66}$ as the product of square roots, separating the $-1$ from $66$ . $\newline$ $\sqrt{-66} = \sqrt{-1 \times 66}$
Use Imaginary Unit: Now, we know that $\sqrt{-1}$ is the imaginary unit $i$ . So we can rewrite the expression as: $\sqrt{-1 \times 66} = i \times \sqrt{66}$
Final Expression: We can't simplify $\sqrt{66}$ any further since $66$ is not a perfect square. So the expression remains: $\newline$ $i \cdot \sqrt{66}$

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