Question

Select all the correct answers.

Which expressions are equivalent to √-27?

Answer 1

the first one and that's the only one

Answer 2

2 Answers: Choice A and choice D

`3i√(3) \ \text{ and } \ i√(27)`

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Work Shown:

We will use the rule that sqrt(A*B) = sqrt(A)*sqrt(B) to get the following

`x = √(-27)\\\\x = √(-1*27)\\\\x = √(-1)*√(27)\\\\x = i√(27) \ \text{ ... one answer; choice D}\\\\x = i√(9*3)\\\\x = i√(9)*√(3)\\\\x = i*3*√(3)\\\\x = 3i√(3) \ \text{ ... another answer; choice A}\\\\`

While choices C and D seem to look equivalent, note how the 'i' is under the square root in choice C. The 'i' term must be outside the root to be equivalent to the original expression. We denote
`i=√(-1)`