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	two billion twenty million eight hundred ninety-three thousand nine hundred ninety-eight

Interesting facts

2020893998 has 16 divisors, whose sum is 3197834640
The reverse of 2020893998 is 8993980202
Previous prime number is 461

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 50
Digital Root 5

Name

Name	one billion four hundred thirty-nine million one hundred twenty-three thousand two hundred eighty-one

Interesting facts

1439123281 has 4 divisors, whose sum is 1439291700
The reverse of 1439123281 is 1823219341
Previous prime number is 9029

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 34
Digital Root 7

Name

Name	two billion fifty-one million eight hundred thirty-six thousand seven hundred forty-three

Interesting facts

2051836743 has 32 divisors, whose sum is 2830888960
The reverse of 2051836743 is 3476381502
Previous prime number is 79

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 39
Digital Root 3

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