Evaluate - square root of -49

Problem

√(,−49)

Solution

1. Identify the expression as the square root of a negative number, which requires the use of the imaginary unit i

2. Apply the property of square roots for negative numbers, where √(,−a)=√(,a)⋅√(,−1) for any positive real number a

3. Substitute the definition of the imaginary unit, where i=√(,−1)

4. Simplify the expression by calculating the square root of the positive constant.

√(,−49)=√(,49)⋅√(,−1)

√(,49)=7

√(,−1)=i

7⋅i=7*i

Final Answer

√(,−49)=7*i

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