Simplify (-8+ square root of -20)/24

Problem

(−8+√(,−20))/24

Solution

1. Express the square root of a negative number using the imaginary unit i where √(,−1)=i

√(,−20)=√(,20)⋅i

2. Simplify the radical by factoring out the largest perfect square from 20.

√(,20)=√(,4⋅5)=2√(,5)

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

(−8+2*i√(,5))/24

4. Factor out the greatest common factor from the terms in the numerator.

2*(−4+i√(,5))

5. Divide the numerator and denominator by their greatest common divisor, which is 2.

(2*(−4+i√(,5)))/24=(−4+i√(,5))/12

Final Answer

(−8+√(,−20))/24=(−4+i√(,5))/12

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