Evaluate square root of -256

Problem

√(,−256)

Solution

1. Identify the expression as the square root of a negative number, which requires the use of the imaginary unit i where i=√(,−1)

2. Rewrite the radicand as a product of the positive value and −1

√(,−256)=√(,256⋅(−1))

3. Apply the product property of radicals to separate the terms.

√(,256⋅(−1))=√(,256)⋅√(,−1)

4. Calculate the square root of the perfect square 256 and substitute i for √(,−1)

√(,256)=16

√(,−1)=i

5. Multiply the results to find the final value.

16⋅i=16*i

Final Answer

√(,−256)=16*i

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