Evaluate square root of -108

Problem

√(,−108)

Solution

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

√(,−108)=√(,108)⋅√(,−1)

√(,−108)=√(,108)*i

2. Factor the radicand 108 into its prime factors to find the largest perfect square divisor.

108=2⋅54=2⋅2⋅27=2⋅3

108=36⋅3

3. Simplify the radical by taking the square root of the perfect square factor.

√(,36⋅3)*i=√(,36)⋅√(,3)*i

6√(,3)*i

Final Answer

√(,−108)=6*i√(,3)

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