Evaluate square root of -12

Problem

√(,−12)

Solution

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

√(,−12)=√(,12)⋅√(,−1)

√(,−12)=√(,12)*i

2. Factor the radicand to find the largest perfect square divisor of 12

√(,12)=√(,4⋅3)

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

√(,4⋅3)=2√(,3)

4. Combine the simplified radical with the imaginary unit.

2√(,3)*i

Final Answer

√(,−12)=2*i√(,3)

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