Evaluate square root of -81

Problem

√(,−81)

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. Rewrite the radicand as a product of a positive number and −1

√(,−81)=√(,81⋅(−1))

3. Apply the product property of radicals to separate the terms.

√(,81⋅(−1))=√(,81)⋅√(,−1)

4. Simplify the square root of the perfect square and substitute i for the square root of −1

√(,81)=9

√(,−1)=i

Final Answer

√(,−81)=9*i

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