Evaluate (-12+ square root of -18)/60

Problem

(−12+√(,−18))/60

Solution

1. Identify the square root of a negative number as an imaginary number using the property √(,−a)=i√(,a)

√(,−18)=i√(,18)

2. Simplify the radical by factoring out the largest perfect square from 18, which is 9.

√(,18)=√(,9⋅2)=3√(,2)

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

(−12+3*i√(,2))/60

4. Factor out the greatest common factor from the numerator, which is 3.

3*(−4+i√(,2))

5. Divide the numerator and denominator by their common factor of 3 to simplify the fraction.

(3*(−4+i√(,2)))/60=(−4+i√(,2))/20

6. Split the expression into its real and imaginary parts.

(−4)/20+(i√(,2))/20

7. Reduce the real part fraction to its simplest form.

−1/5+√(,2)/20*i

Final Answer

(−12+√(,−18))/60=−1/5+√(,2)/20*i

Want more problems? Check here!