Evaluate square root of -81 square root of -144

Problem

√(,−81)√(,−144)

Solution

1. Express the square roots of negative numbers in terms of the imaginary unit i where i=√(,−1)

2. Simplify the first radical by taking the square root of the positive constant and multiplying by i

√(,−81)=√(,81)⋅√(,−1)=9*i

3. Simplify the second radical using the same method.

√(,−144)=√(,144)⋅√(,−1)=12*i

4. Multiply the two resulting imaginary numbers together.

9*i⋅12*i=108*i^2

5. Substitute the value i^2=−1 into the expression to find the final real number.

108*(−1)=−108

Final Answer

√(,−81)√(,−144)=−108

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