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

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Algebra

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

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	three hundred sixty-three million seven hundred seventy-eight thousand two hundred eighty

Interesting facts

363778280 has 64 divisors, whose sum is 1507572000
The reverse of 363778280 is 082877363
Previous prime number is 43

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 44
Digital Root 8

Name

Name	two hundred thirteen million two hundred forty thousand thirty-six

Interesting facts

213240036 has 16 divisors, whose sum is 639720144
The reverse of 213240036 is 630042312
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 21
Digital Root 3

Name

Name	seven hundred seventy-four million seven hundred forty-four thousand five hundred forty-seven

Interesting facts

774744547 has 8 divisors, whose sum is 795304640
The reverse of 774744547 is 745447477
Previous prime number is 73

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 49
Digital Root 4

Write as a Single Logarithm 2( log base 3 of 8+ log base 3 of z)- log base 3 of 3^4-7^2

Find the Roots (Zeros) y=x^3-5x^2+9x-45

Find the Discriminant -7x^2+8x+2

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