Evaluate square root of -14

Problem

√(,−14)

Solution

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

2. Apply the property of square roots for negative numbers, √(,−a)=i√(,a) for any positive real number a

3. Rewrite the expression by factoring out the square root of −1

√(,−14)=√(,−1⋅14)

4. Simplify the expression by replacing √(,−1) with i

√(,−14)=i√(,14)

Final Answer

√(,−14)=i√(,14)

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