Simplify (-12 square root of 30)/(3 square root of 6)

$\frac{- 12 \sqrt{30}}{3 \sqrt{6}}$

Step 1

Cancel the common factor of $- 12$ and $3$ .

Factor $3$ out of $- 12 \sqrt{30}$ .

$\frac{3 (- 4 \sqrt{30})}{3 \sqrt{6}}$

Cancel the common factors.

Factor $3$ out of $3 \sqrt{6}$ .

$\frac{3 (- 4 \sqrt{30})}{3 (\sqrt{6})}$

Cancel the common factor.

$\frac{3 (- 4 \sqrt{30})}{3 \sqrt{6}}$

Rewrite the expression.

$\frac{- 4 \sqrt{30}}{\sqrt{6}}$

Step 2

Combine $\sqrt{30}$ and $\sqrt{6}$ into a single radical.

$- 4 \sqrt{\frac{30}{6}}$

Step 3

Divide $30$ by $6$ .

$- 4 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 4 \sqrt{5}$

Decimal Form:

$- 8.94427190 \dots$