Simplify 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 12 into its prime factors to find the largest perfect square.

12=4⋅3

3. Apply the product property of square roots to separate the perfect square.

√(,12)*i=√(,4⋅3)*i

√(,12)*i=√(,4)⋅√(,3)*i

4. Simplify the square root of the perfect square 4

√(,4)=2

2⋅√(,3)*i=2*i√(,3)

Final Answer

√(,−12)=2*i√(,3)

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