Evaluate 2 square root of -108

Problem

2√(,−108)

Solution

1. Identify the imaginary unit by using the property √(,−a)=i√(,a) for a>0

2√(,−108)=2*i√(,108)

2. Factor the radicand to find the largest perfect square divisor.

108=36⋅3

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

√(,108)=√(,36⋅3)=6√(,3)

4. Multiply the resulting terms together to find the final simplified form.

2*i⋅6√(,3)=12*i√(,3)

Final Answer

2√(,−108)=12*i√(,3)

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