Evaluate square root of -8

Problem

√(,−8)

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 a positive number and −1

√(,−8)=√(,8⋅(−1))

3. Apply the product property of radicals to separate the real and imaginary parts.

√(,8⋅(−1))=√(,8)⋅√(,−1)

4. Substitute i for √(,−1)

√(,8)⋅i

5. Simplify the radical √(,8) by factoring out the largest perfect square, which is 4

√(,4⋅2)⋅i

6. Evaluate the square root of the perfect square.

2√(,2)*i

Final Answer

√(,−8)=2*i√(,2)

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