Evaluate square root of -27

Problem

√(,−27)

Solution

1. Identify the square root of a negative number by using the imaginary unit i where √(,−1)=i

√(,−27)=√(,27)⋅√(,−1)

√(,−27)=√(,27)*i

2. Factor the radicand into a perfect square and a remaining factor to simplify the radical.

√(,27)=√(,9⋅3)

3. Simplify the square root of the perfect square.

√(,9⋅3)=3√(,3)

4. Combine the simplified radical with the imaginary unit.

3√(,3)*i

Final Answer

√(,−27)=3*i√(,3)

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