Question

What is equivalent to the square root of -27?

Answer 1

$\sqrt{ - 27 } = \sqrt{ - (3 \times 3 \times 3)} \\ \\ = \sqrt{ - 3 \times - 3 \times - 3} \\ = \sqrt{9 \times -3 } \\ = 3 \sqrt{ - 3}$

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If you want to further rationalize.

then follow:

$= 3 \sqrt{ - 3} \\ = 3 \sqrt{ -3} \times \sqrt{ - 3 } \\ = 3 \times ( \sqrt{ - 3 } ) {}^{2} \\ = 3 \times ( - 3) \\ = - 9$