Evaluate

Problem

(√(,−7)√(,−49))/√(,28)

Solution

1. Express the square roots of negative numbers using the imaginary unit i where √(,−a)=i√(,a) for a>0

√(,−7)=i√(,7)

√(,−49)=i√(,49)=7*i

2. Substitute these values back into the numerator of the expression.

i√(,7)⋅7*i=7*i2√(,7)

3. Apply the property i2=−1 to simplify the numerator.

7*(−1)√(,7)=−7√(,7)

4. Simplify the denominator by factoring out the largest perfect square from the radicand.

√(,28)=√(,4⋅7)=2√(,7)

5. Divide the simplified numerator by the simplified denominator and cancel the common factor √(,7)

(−7√(,7))/(2√(,7))=−7/2

Final Answer

(√(,−7)√(,−49))/√(,28)=−7/2

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