Evaluate square root of -80

Problem

√(,−80)

Solution

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

√(,−80)=√(,80)⋅√(,−1)

√(,−80)=√(,80)*i

2. Factor the radicand 80 to find the largest perfect square factor.

80=16⋅5

3. Simplify the radical by taking the square root of the perfect square.

√(,16⋅5)*i=√(,16)⋅√(,5)*i

4√(,5)*i

Final Answer

√(,−80)=4*i√(,5)

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