Evaluate square root of -13

Problem

√(,−13)

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 radicals for negative numbers, √(,−a)=√(,−1)⋅√(,a)=i√(,a)

3. Substitute the value 13 into the property to get i√(,13)

4. Simplify the radical if possible; since 13 is a prime number, the radical cannot be simplified further.

Final Answer

√(,−13)=i√(,13)

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