Evaluate square root of -16

Problem

√(,−16)

Solution

1. Identify the expression as the square root of a negative number, which involves the imaginary unit i where i=√(,−1)

2. Apply the product property of square roots to separate the negative sign from the magnitude of the number.

√(,−16)=√(,16⋅(−1))

3. Distribute the square root across the factors.

√(,16⋅(−1))=√(,16)⋅√(,−1)

4. Simplify the square root of the positive constant and substitute i for the square root of negative one.

√(,16)⋅√(,−1)=4*i

Final Answer

√(,−16)=4*i

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