Simplify (-2/3* square root of 6)(9 square root of 3)

$(- \frac{2}{3} \cdot \sqrt{6}) (9 \sqrt{3})$

Step 1

Combine $\sqrt{6}$ and $\frac{2}{3}$ .

$- \frac{\sqrt{6} \cdot 2}{3} (9 \sqrt{3})$

Step 2

Move $2$ to the left of $\sqrt{6}$ .

$- \frac{2 \sqrt{6}}{3} (9 \sqrt{3})$

Step 3

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2 \sqrt{6}}{3}$ into the numerator.

$\frac{- 2 \sqrt{6}}{3} (9 \sqrt{3})$

Factor $3$ out of $9 \sqrt{3}$ .

$\frac{- 2 \sqrt{6}}{3} (3 (3 \sqrt{3}))$

Cancel the common factor.

$\frac{- 2 \sqrt{6}}{3} (3 (3 \sqrt{3}))$

Rewrite the expression.

$- 2 \sqrt{6} (3 \sqrt{3})$

Step 4

Multiply $3$ by $- 2$ .

$- 6 \sqrt{6} \sqrt{3}$

Step 5

Combine using the product rule for radicals.

$- 6 \sqrt{3 \cdot 6}$

Step 6

Multiply $3$ by $6$ .

$- 6 \sqrt{18}$

Step 7

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

Factor $9$ out of $18$ .

$- 6 \sqrt{9 (2)}$

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

$- 6 \sqrt{3^{2} \cdot 2}$

Step 8

Pull terms out from under the radical.

$- 6 (3 \sqrt{2})$

Step 9

Multiply $3$ by $- 6$ .

$- 18 \sqrt{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- 18 \sqrt{2}$

Decimal Form:

$- 25.45584412 \dots$