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

Problem

(−6+√(,−54))/3

Solution

1. Express the square root of a negative number using the imaginary unit i

√(,−54)=√(,−1⋅54)

√(,−54)=i√(,54)

2. Simplify the radical by factoring out the largest perfect square.

√(,54)=√(,9⋅6)

√(,54)=3√(,6)

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

(−6+3*i√(,6))/3

4. Divide each term in the numerator by the denominator to simplify the fraction.

(−6)/3+(3*i√(,6))/3

−2+i√(,6)

Final Answer

(−6+√(,−54))/3=−2+i√(,6)

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