What is (-8 + √(-20) )/(24)?

Question

What is
`(-8 + √(-20) )/(24)`?

Answer 1

`\displaystyle (-4 + i√(5))/(12)`

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Factoring

Algebra II

• Imaginary Numbers: √-1 = i

Explanation:

Step 1: Define

`\displaystyle (-8 + √(-20))/(24)`

Step 2: Simplify

1. [Fraction] [√Radical] Factor:
   `\displaystyle (-8 + √(-1)√(20))/(24)`
2. [Fraction] [√Radical] Evaluate:
   `\displaystyle (-8 + i√(20))/(24)`
3. [Fraction] [√Radical] Simplify:
   `\displaystyle (-8 + 2i√(5))/(24)`
4. [Fraction] Factor numerator:
   `\displaystyle (2(-4 + i√(5)))/(24)`
5. [Fraction] Simplify:
   `\displaystyle (-4 + i√(5))/(12)`