Evaluate square root of -180

Problem

√(,−180)

Solution

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

√(,−180)=i√(,180)

2. Factor the radicand to find the largest perfect square divisor of 180

180=36⋅5

3. Apply the product property of square roots, which states √(,a⋅b)=√(,a)⋅√(,b)

i√(,36⋅5)=i√(,36)√(,5)

4. Simplify the square root of the perfect square 36

√(,36)=6

5. Combine the terms into the final simplified form.

i⋅6⋅√(,5)=6*i√(,5)

Final Answer

√(,−180)=6*i√(,5)

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