Evaluate (-20+ square root of -75)/40

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Algebra

$\frac{- 20 + \sqrt{- 75}}{40}$

Pull out imaginary unit $i$ .

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Rewrite $- 75$ as $- 1 (75)$ .

$\frac{- 20 + \sqrt{- 1 (75)}}{40}$

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

$\frac{- 20 + \sqrt{- 1} \cdot \sqrt{75}}{40}$

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

$\frac{- 20 + i \cdot \sqrt{75}}{40}$

Simplify the numerator.

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Rewrite $75$ as $5^{2} \cdot 3$ .

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Factor $25$ out of $75$ .

$\frac{- 20 + i \cdot \sqrt{25 (3)}}{40}$

Rewrite $25$ as $5^{2}$ .

$\frac{- 20 + i \cdot \sqrt{5^{2} \cdot 3}}{40}$

Pull terms out from under the radical.

$\frac{- 20 + i \cdot (5 \sqrt{3})}{40}$

Move $5$ to the left of $i$ .

$\frac{- 20 + 5 i \sqrt{3}}{40}$

Simplify terms.

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Cancel the common factor of $- 20 + 5 i \sqrt{3}$ and $40$ .

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Factor $5$ out of $- 20$ .

$\frac{5 \cdot - 4 + 5 i \sqrt{3}}{40}$

Factor $5$ out of $5 i \sqrt{3}$ .

$\frac{5 \cdot - 4 + 5 (i \sqrt{3})}{40}$

Factor $5$ out of $5 \cdot - 4 + 5 (i \sqrt{3})$ .

$\frac{5 \cdot (- 4 + i \sqrt{3})}{40}$

Cancel the common factors.

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Factor $5$ out of $40$ .

$\frac{5 \cdot (- 4 + i \sqrt{3})}{5 (8)}$

Cancel the common factor.

$\frac{5 \cdot (- 4 + i \sqrt{3})}{5 \cdot 8}$

Rewrite the expression.

$\frac{- 4 + i \sqrt{3}}{8}$

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

$\frac{- 1 (4) + i \sqrt{3}}{8}$

Factor $- 1$ out of $i \sqrt{3}$ .

$\frac{- 1 (4) - (- i \sqrt{3})}{8}$

Factor $- 1$ out of $- 1 (4) - (- i \sqrt{3})$ .

$\frac{- 1 (4 - i \sqrt{3})}{8}$

Move the negative in front of the fraction.

$- \frac{4 - i \sqrt{3}}{8}$

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Name

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

Interesting facts

1827352550 has 32 divisors, whose sum is 3386665728
The reverse of 1827352550 is 0552537281
Previous prime number is 53

Basic properties

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

Name

Name	eight hundred fifty-three million nine hundred twenty-eight thousand one hundred eighty-seven

Interesting facts

853928187 has 16 divisors, whose sum is 1302282240
The reverse of 853928187 is 781829358
Previous prime number is 1279

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 51
Digital Root 6

Name

Name	two hundred seventy-four million eight hundred thirty-three thousand thirty-one

Interesting facts

274833031 has 16 divisors, whose sum is 304197120
The reverse of 274833031 is 130338472
Previous prime number is 239

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 31
Digital Root 4

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