Simplify (-3+ square root of -27)/3

Problem

(−3+√(,−27))/3

Solution

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

√(,−27)=√(,27)⋅i

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

√(,27)=√(,9⋅3)=3√(,3)

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

(−3+3*i√(,3))/3

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

3*(−1+i√(,3))

5. Divide the numerator and denominator by 3 to reach the simplest form.

−1+i√(,3)

Final Answer

(−3+√(,−27))/3=−1+i√(,3)

Want more problems? Check here!