Evaluate square root of -196

Problem

√(,−196)

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)=√(,a)⋅√(,−1)=√(,a)⋅i

3. Rewrite the expression using this property.

√(,−196)=√(,196)⋅i

4. Calculate the square root of the positive constant 196

√(,196)=14

5. Combine the result with the imaginary unit.

14⋅i=14*i

Final Answer

√(,−196)=14*i

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