Simplify -3 square root of 7r^3*6 square root of 7r^2

$- 3 \sqrt{7 r^{3}} \cdot 6 \sqrt{7 r^{2}}$

Step 1

Rewrite $7 r^{3}$ as $r^{2} \cdot (7 r)$ .

Factor out $r^{2}$ .

$- 3 \sqrt{7 (r^{2} r)} \cdot (6 \sqrt{7 r^{2}})$

Reorder $7$ and $r^{2}$ .

$- 3 \sqrt{r^{2} \cdot 7 r} \cdot (6 \sqrt{7 r^{2}})$

Add parentheses.

$- 3 \sqrt{r^{2} \cdot (7 r)} \cdot (6 \sqrt{7 r^{2}})$

Step 2

Pull terms out from under the radical.

$- 3 (r \sqrt{7 r}) \cdot (6 \sqrt{7 r^{2}})$

Step 3

Reorder $7$ and $r^{2}$ .

$- 3 r \sqrt{7 r} \cdot (6 \sqrt{r^{2} \cdot 7})$

Step 4

Pull terms out from under the radical.

$- 3 r \sqrt{7 r} \cdot (6 (r \sqrt{7}))$

Step 5

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

$- 3 (r \cdot r) \sqrt{7 r} \cdot (6 (\sqrt{7}))$

Multiply $r$ by $r$ .

$- 3 r^{2} \sqrt{7 r} \cdot (6 (\sqrt{7}))$

Step 6

Multiply $- 3 r^{2} \sqrt{7 r} (6 \sqrt{7})$ .

Multiply $6$ by $- 3$ .

$- 18 r^{2} \sqrt{7 r} \sqrt{7}$

Combine using the product rule for radicals.

$- 18 r^{2} \sqrt{7 (7 r)}$

Multiply $7$ by $7$ .

$- 18 r^{2} \sqrt{49 r}$

Step 7

Rewrite $49$ as $7^{2}$ .

$- 18 r^{2} \sqrt{7^{2} r}$

Step 8

Pull terms out from under the radical.

$- 18 r^{2} (7 \sqrt{r})$

Step 9

Multiply $7$ by $- 18$ .

$- 126 r^{2} \sqrt{r}$