Evaluate square root of -2

Problem

√(,−2)

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. Apply the property of radicals for negative numbers, which states √(,−a)=√(,−1)⋅√(,a) for any positive real number a

3. Substitute i for √(,−1) to rewrite the expression in terms of imaginary numbers.

4. Simplify the resulting expression by keeping the radical in its simplest form.

Final Answer

√(,−2)=i√(,2)

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