Evaluate square root of -169

Problem

√(,−169)

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)=√(,−1)⋅√(,a)=i√(,a)

3. Rewrite the expression using this property.

√(,−169)=√(,169)⋅√(,−1)

4. Calculate the square root of the positive constant 169

√(,169)=13

5. Substitute the value back into the expression and include the imaginary unit.

√(,−169)=13*i

Final Answer

√(,−169)=13*i

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