Evaluate square root of -7 square root of -28

Problem

√(,−7)√(,−28)

Solution

1. Express in terms of the imaginary unit i by using the property √(,−a)=i√(,a) for any positive real number a

√(,−7)=i√(,7)

√(,−28)=i√(,28)

2. Multiply the expressions together, grouping the imaginary units and the radicals.

i√(,7)⋅i√(,28)=i2√(,7⋅28)

3. Simplify the power of i using the identity i2=−1

−1⋅√(,7⋅28)

4. Simplify the radicand by factoring 28 into 4⋅7

−1⋅√(,7⋅4⋅7)

−1⋅√(,4⋅49)

5. Evaluate the square root of the perfect squares.

−1⋅2⋅7

−14

Final Answer

√(,−7)√(,−28)=−14

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