Evaluate - square root of -81

Problem

−√(,−81)

Solution

1. Identify the expression as the negative of the square root of a negative number.

2. Apply the definition of the imaginary unit i where √(,−1)=i

3. Rewrite the square root of the negative number using the property √(,−a)=√(,a)⋅√(,−1) for a>0

√(,−81)=√(,81)⋅√(,−1)

4. Simplify the square root of the perfect square 81

√(,81)=9

5. Substitute the values back into the expression, keeping the negative sign outside the radical.

−(9*i)=−9*i

Final Answer

−√(,−81)=−9*i

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