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 where i=√(,−1)

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

√(,−49)=√(,49⋅(−1))

3. Apply the product property of square roots, √(,a⋅b)=√(,a)⋅√(,b)

√(,49⋅(−1))=√(,49)⋅√(,−1)

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

√(,49)⋅√(,−1)=7⋅i

Final Answer

√(,−49)=7*i

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