Evaluate (-12+ square root of -18)/60

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$\frac{- 12 + \sqrt{- 18}}{60}$

Pull out imaginary unit $i$ .

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Rewrite $- 18$ as $- 1 (18)$ .

$\frac{- 12 + \sqrt{- 1 (18)}}{60}$

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$\frac{- 12 + \sqrt{- 1} \cdot \sqrt{18}}{60}$

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

$\frac{- 12 + i \cdot \sqrt{18}}{60}$

Simplify the numerator.

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Rewrite $18$ as $3^{2} \cdot 2$ .

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Factor $9$ out of $18$ .

$\frac{- 12 + i \cdot \sqrt{9 (2)}}{60}$

Rewrite $9$ as $3^{2}$ .

$\frac{- 12 + i \cdot \sqrt{3^{2} \cdot 2}}{60}$

Pull terms out from under the radical.

$\frac{- 12 + i \cdot (3 \sqrt{2})}{60}$

Move $3$ to the left of $i$ .

$\frac{- 12 + 3 i \sqrt{2}}{60}$

Simplify terms.

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Cancel the common factor of $- 12 + 3 i \sqrt{2}$ and $60$ .

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Factor $3$ out of $- 12$ .

$\frac{3 \cdot - 4 + 3 i \sqrt{2}}{60}$

Factor $3$ out of $3 i \sqrt{2}$ .

$\frac{3 \cdot - 4 + 3 (i \sqrt{2})}{60}$

Factor $3$ out of $3 \cdot - 4 + 3 (i \sqrt{2})$ .

$\frac{3 \cdot (- 4 + i \sqrt{2})}{60}$

Cancel the common factors.

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Factor $3$ out of $60$ .

$\frac{3 \cdot (- 4 + i \sqrt{2})}{3 (20)}$

Cancel the common factor.

$\frac{3 \cdot (- 4 + i \sqrt{2})}{3 \cdot 20}$

Rewrite the expression.

$\frac{- 4 + i \sqrt{2}}{20}$

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

$\frac{- 1 (4) + i \sqrt{2}}{20}$

Factor $- 1$ out of $i \sqrt{2}$ .

$\frac{- 1 (4) - (- i \sqrt{2})}{20}$

Factor $- 1$ out of $- 1 (4) - (- i \sqrt{2})$ .

$\frac{- 1 (4 - i \sqrt{2})}{20}$

Move the negative in front of the fraction.

$- \frac{4 - i \sqrt{2}}{20}$

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Name

Name	one billion two hundred fifty-six million three hundred thirteen thousand six hundred fifty-three

Interesting facts

1256313653 has 8 divisors, whose sum is 1436837760
The reverse of 1256313653 is 3563136521
Previous prime number is 1381

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 35
Digital Root 8

Name

Name	one hundred eighty-eight million four hundred forty-two thousand one hundred thirty-two

Interesting facts

188442132 has 32 divisors, whose sum is 568717632
The reverse of 188442132 is 231244881
Previous prime number is 167

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 33
Digital Root 6

Name

Name	one billion one hundred ninety-eight million nine hundred seventeen thousand one hundred thirteen

Interesting facts

1198917113 has 4 divisors, whose sum is 1251043968
The reverse of 1198917113 is 3117198911
Previous prime number is 23

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 41
Digital Root 5

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