Evaluate square root of -32

Problem

√(,−32)

Solution

1. Identify the negative radicand, which indicates that the result will involve the imaginary unit i where i=√(,−1)

2. Rewrite the expression by factoring out −1 from the square root.

√(,−32)=√(,32)⋅√(,−1)

3. Substitute i for √(,−1)

√(,32)⋅√(,−1)=i√(,32)

4. Factor the number 32 to find the largest perfect square.

32=16⋅2

5. Simplify the square root by taking the square root of the perfect square.

i√(,16⋅2)=i⋅4√(,2)

6. Rearrange the terms into standard form b*i

4*i√(,2)

Final Answer

√(,−32)=4*i√(,2)

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