Evaluate (-12+ square root of -45)/24

Solve Math

Algebra

$\frac{- 12 + \sqrt{- 45}}{24}$

Pull out imaginary unit $i$ .

Tap for more steps...

Rewrite $- 45$ as $- 1 (45)$ .

$\frac{- 12 + \sqrt{- 1 (45)}}{24}$

Rewrite $\sqrt{- 1 (45)}$ as $\sqrt{- 1} \cdot \sqrt{45}$ .

$\frac{- 12 + \sqrt{- 1} \cdot \sqrt{45}}{24}$

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

$\frac{- 12 + i \cdot \sqrt{45}}{24}$

Simplify the numerator.

Tap for more steps...

Rewrite $45$ as $3^{2} \cdot 5$ .

Tap for more steps...

Factor $9$ out of $45$ .

$\frac{- 12 + i \cdot \sqrt{9 (5)}}{24}$

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

$\frac{- 12 + i \cdot \sqrt{3^{2} \cdot 5}}{24}$

Pull terms out from under the radical.

$\frac{- 12 + i \cdot (3 \sqrt{5})}{24}$

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

$\frac{- 12 + 3 i \sqrt{5}}{24}$

Simplify terms.

Tap for more steps...

Cancel the common factor of $- 12 + 3 i \sqrt{5}$ and $24$ .

Tap for more steps...

Factor $3$ out of $- 12$ .

$\frac{3 \cdot - 4 + 3 i \sqrt{5}}{24}$

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

$\frac{3 \cdot - 4 + 3 (i \sqrt{5})}{24}$

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

$\frac{3 \cdot (- 4 + i \sqrt{5})}{24}$

Cancel the common factors.

Tap for more steps...

Factor $3$ out of $24$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 4 + i \sqrt{5}}{8}$

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

$\frac{- 1 (4) + i \sqrt{5}}{8}$

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

$\frac{- 1 (4) - (- i \sqrt{5})}{8}$

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

$\frac{- 1 (4 - i \sqrt{5})}{8}$

Move the negative in front of the fraction.

$- \frac{4 - i \sqrt{5}}{8}$

Do you know how to Evaluate (-12+ square root of -45)/24? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Evaluate log of 2

Solve Using the Quadratic Formula x^2+x-1=0

Solve by Completing the Square x^2-10x-4=0

Find the Inverse Function f(x)=x^3-5

Evaluate square root of -300