Evaluate square root of -40

Problem

√(,−40)

Solution

1. Identify the square root of a negative number by using the imaginary unit i where √(,−1)=i

√(,−40)=√(,40)⋅√(,−1)

√(,−40)=√(,40)*i

2. Factor the radicand 40 into its prime factors or look for the largest perfect square factor.

40=4⋅10

3. Apply the product property of square roots to separate the perfect square.

√(,40)*i=√(,4⋅10)*i

√(,40)*i=√(,4)⋅√(,10)*i

4. Simplify the square root of the perfect square 4

√(,4)=2

2⋅√(,10)*i=2*i√(,10)

Final Answer

√(,−40)=2*i√(,10)

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