Question

what is $\frac{-8 + \sqrt{-20} }{24}$?

Answer 1

Answer:

$\displaystyle \frac{-4 + i\sqrt{5}}{12}$

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

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{-8 + \sqrt{-20}}{24}$

Step 2: Simplify

1. [Fraction] [√Radical] Factor:                                                                           $\displaystyle \frac{-8 + \sqrt{-1}\sqrt{20}}{24}$
2. [Fraction] [√Radical] Evaluate:                                                                       $\displaystyle \frac{-8 + i\sqrt{20}}{24}$
3. [Fraction] [√Radical] Simplify:                                                                        $\displaystyle \frac{-8 + 2i\sqrt{5}}{24}$
4. [Fraction] Factor numerator:                                                                          $\displaystyle \frac{2(-4 + i\sqrt{5})}{24}$
5. [Fraction] Simplify:                                                                                          $\displaystyle \frac{-4 + i\sqrt{5}}{12}$