Evaluate (-20+ square root of -50)/60

Problem

(−20+√(,−50))/60

Solution

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

√(,−50)=i√(,50)

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

√(,50)=√(,25⋅2)=5√(,2)

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

(−20+5*i√(,2))/60

4. Factor out the greatest common divisor from the numerator to prepare for simplification.

(5*(−4+i√(,2)))/60

5. Reduce the fraction by dividing both the numerator and the denominator by 5.

(−4+i√(,2))/12

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

(−4)/12+(i√(,2))/12

7. Simplify the real part by reducing the fraction.

−1/3+(i√(,2))/12

Final Answer

(−20+√(,−50))/60=−1/3+(i√(,2))/12

Want more problems? Check here!