Simplify -3 square root of 20*7 square root of 8

$- 3 \sqrt{20} \cdot 7 \sqrt{8}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$- 3 \sqrt{4 (5)} \cdot (7 \sqrt{8})$

Rewrite $4$ as $2^{2}$ .

$- 3 \sqrt{2^{2} \cdot 5} \cdot (7 \sqrt{8})$

$- 3 \sqrt{2^{2} \cdot 5} \cdot (7 \sqrt{8})$

Pull terms out from under the radical.

$- 3 (2 \sqrt{5}) \cdot (7 \sqrt{8})$

Multiply $2$ by $- 3$ .

$- 6 \sqrt{5} \cdot (7 \sqrt{8})$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$- 6 \sqrt{5} \cdot (7 \sqrt{4 (2)})$

Rewrite $4$ as $2^{2}$ .

$- 6 \sqrt{5} \cdot (7 \sqrt{2^{2} \cdot 2})$

$- 6 \sqrt{5} \cdot (7 \sqrt{2^{2} \cdot 2})$

Pull terms out from under the radical.

$- 6 \sqrt{5} \cdot (7 (2 \sqrt{2}))$

Multiply $2$ by $7$ .

$- 6 \sqrt{5} \cdot (14 \sqrt{2})$

Multiply $- 6 \sqrt{5} (14 \sqrt{2})$ .

Multiply $14$ by $- 6$ .

$- 84 \sqrt{5} \sqrt{2}$

Combine using the product rule for radicals.

$- 84 \sqrt{2 \cdot 5}$

Multiply $2$ by $5$ .

$- 84 \sqrt{10}$

$- 84 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$- 84 \sqrt{10}$

Decimal Form:

$- 265.63132345 \dots$

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