Evaluate square root of -175

Problem

√(,−175)

Solution

1. Identify the square root of a negative number by using the imaginary unit i where √(,−1)=i

√(,−175)=√(,175)⋅√(,−1)

√(,−175)=i√(,175)

2. Factor the radicand to find the largest perfect square divisor.

175=25⋅7

3. Simplify the radical by taking the square root of the perfect square factor.

√(,175)=√(,25⋅7)

√(,175)=5√(,7)

4. Combine the results to express the final answer in terms of i

i⋅5√(,7)=5*i√(,7)

Final Answer

√(,−175)=5*i√(,7)

Want more problems? Check here!