Evaluate square root of -18

Problem

√(,−18)

Solution

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

√(,−18)=√(,18)⋅√(,−1)

√(,−18)=√(,18)*i

2. Factor the radicand into a product of its prime factors or a perfect square and a remaining factor.

√(,18)=√(,9⋅2)

3. Simplify the square root of the perfect square.

√(,9⋅2)=√(,9)⋅√(,2)

√(,9)⋅√(,2)=3√(,2)

4. Combine the simplified radical with the imaginary unit.

3√(,2)*i

Final Answer

√(,−18)=3*i√(,2)

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