Evaluate square root of -125

Problem

√(,−125)

Solution

1. Identify the negative radicand and rewrite the expression using the imaginary unit i where i=√(,−1)

√(,−125)=√(,125)⋅√(,−1)

√(,−125)=√(,125)*i

2. Factor the number inside the square root to find the largest perfect square divisor.

125=25⋅5

3. Apply the product property of square roots to separate the perfect square.

√(,25⋅5)*i=√(,25)⋅√(,5)*i

4. Simplify the square root of the perfect square.

√(,25)⋅√(,5)*i=5√(,5)*i

Final Answer

√(,−125)=5*i√(,5)

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