Evaluate - square root of -100

Problem

√(,−100)

Solution

1. Identify the expression as the square root of a negative number, which requires the use of the imaginary unit i

2. Apply the property of square roots for negative numbers, which states that √(,−a)=√(,a)⋅√(,−1) for any positive real number a

3. Substitute the definition of the imaginary unit, where i=√(,−1)

4. Simplify the expression by calculating the square root of the positive real number.

√(,−100)=√(,100)⋅√(,−1)

√(,−100)=10*i

Final Answer

√(,−100)=10*i

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