Evaluate square root of -49-4

Problem

√(,−49−4)

Solution

1. Simplify the expression inside the square root by performing the subtraction.

−49−4=−53

2. Rewrite the square root of the negative number using the imaginary unit i where i=√(,−1)

√(,−53)=√(,−1⋅53)

3. Apply the product property of square roots to separate the imaginary part.

√(,−1⋅53)=√(,53)⋅√(,−1)

4. Substitute i for √(,−1) to express the result in terms of complex numbers.

√(,53)⋅i=i√(,53)

Final Answer

√(,−49−4)=i√(,53)

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