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

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Algebra

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

Pull out imaginary unit $i$ .

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Rewrite $- 20$ as $- 1 (20)$ .

$\frac{- 8 + \sqrt{- 1 (20)}}{24}$

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$\frac{- 8 + \sqrt{- 1} \cdot \sqrt{20}}{24}$

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{- 8 + i \cdot \sqrt{20}}{24}$

Simplify the numerator.

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Rewrite $20$ as $2^{2} \cdot 5$ .

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Factor $4$ out of $20$ .

$\frac{- 8 + i \cdot \sqrt{4 (5)}}{24}$

Rewrite $4$ as $2^{2}$ .

$\frac{- 8 + i \cdot \sqrt{2^{2} \cdot 5}}{24}$

Pull terms out from under the radical.

$\frac{- 8 + i \cdot (2 \sqrt{5})}{24}$

Move $2$ to the left of $i$ .

$\frac{- 8 + 2 i \sqrt{5}}{24}$

Simplify terms.

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Cancel the common factor of $- 8 + 2 i \sqrt{5}$ and $24$ .

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Factor $2$ out of $- 8$ .

$\frac{2 \cdot - 4 + 2 i \sqrt{5}}{24}$

Factor $2$ out of $2 i \sqrt{5}$ .

$\frac{2 \cdot - 4 + 2 (i \sqrt{5})}{24}$

Factor $2$ out of $2 \cdot - 4 + 2 (i \sqrt{5})$ .

$\frac{2 \cdot (- 4 + i \sqrt{5})}{24}$

Cancel the common factors.

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Factor $2$ out of $24$ .

$\frac{2 \cdot (- 4 + i \sqrt{5})}{2 (12)}$

Cancel the common factor.

$\frac{2 \cdot (- 4 + i \sqrt{5})}{2 \cdot 12}$

Rewrite the expression.

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

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (4) + i \sqrt{5}}{12}$

Factor $- 1$ out of $i \sqrt{5}$ .

$\frac{- 1 (4) - (- i \sqrt{5})}{12}$

Factor $- 1$ out of $- 1 (4) - (- i \sqrt{5})$ .

$\frac{- 1 (4 - i \sqrt{5})}{12}$

Move the negative in front of the fraction.

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

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Name

Name	three hundred fifty-three million four hundred one thousand one hundred forty-three

Interesting facts

353401143 has 4 divisors, whose sum is 471201528
The reverse of 353401143 is 341104353
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 24
Digital Root 6

Name

Name	one hundred eighteen million eighty-one thousand eight hundred twenty-six

Interesting facts

118081826 has 4 divisors, whose sum is 177122742
The reverse of 118081826 is 628180811
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 35
Digital Root 8

Name

Name	two billion seventy-eight million seven hundred twenty-one thousand three hundred eight

Interesting facts

2078721308 has 32 divisors, whose sum is 5067423504
The reverse of 2078721308 is 8031278702
Previous prime number is 43

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 38
Digital Root 2

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