Evaluate (-6+ square root of -54)/3

Problem

(−6+√(,−54))/3

Solution

1. Simplify the radical by expressing the square root of a negative number using the imaginary unit i

√(,−54)=√(,−1⋅9⋅6)

√(,−54)=3*i√(,6)

2. Substitute the simplified radical back into the original expression.

(−6+3*i√(,6))/3

3. Factor out the common factor of 3 from the numerator.

3*(−2+i√(,6))

4. Divide the numerator and denominator by 3 to simplify the fraction.

−2+i√(,6)

Final Answer

(−6+√(,−54))/3=−2+i√(,6)

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