Evaluate square root of -216

Problem

√(,−216)

Solution

1. Identify the negative radicand and rewrite the expression using the imaginary unit i where i=√(,−1)

√(,−216)=√(,216)⋅√(,−1)

√(,−216)=i√(,216)

2. Factor the number 216 to find the largest perfect square divisor.

216=36⋅6

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

√(,216)=√(,36⋅6)

√(,216)=6√(,6)

4. Combine the simplified radical with the imaginary unit to reach the final form.

i√(,216)=6*i√(,6)

Final Answer

√(,−216)=6*i√(,6)

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