Evaluate square root of -25

Problem

√(,−25)

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

√(,−25)=√(,25⋅(−1))

3. Apply the product property of radicals, √(,a⋅b)=√(,a)⋅√(,b)

√(,25⋅(−1))=√(,25)⋅√(,−1)

4. Simplify the square root of the positive constant and substitute i for √(,−1)

√(,25)⋅√(,−1)=5*i

Final Answer

√(,−25)=5*i

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