Evaluate square root of -50

Problem

√(,−50)

Solution

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

√(,−50)=√(,−1⋅50)

√(,−50)=i√(,50)

2. Factor the radicand to find the largest perfect square divisor of 50

√(,50)=√(,25⋅2)

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

√(,25⋅2)=5√(,2)

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

i⋅5√(,2)=5*i√(,2)

Final Answer

√(,−50)=5*i√(,2)

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