Evaluate square root of -200

Problem

√(,−200)

Solution

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

√(,−200)=√(,200)⋅√(,−1)

√(,−200)=√(,200)*i

2. Factor the radicand to find the largest perfect square divisor of 200

200=100⋅2

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

√(,100⋅2)*i=√(,100)⋅√(,2)*i

4. Simplify the square root of the perfect square.

√(,100)=10

5. Combine the terms into the final simplified form.

10⋅√(,2)*i=10*i√(,2)

Final Answer

√(,−200)=10*i√(,2)

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