Simplify -2 square root of 10*3 square root of 20

$- 2 \sqrt{10} \cdot 3 \sqrt{20}$

Step 1

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

Factor $4$ out of $20$ .

$- 2 \sqrt{10} \cdot (3 \sqrt{4 (5)})$

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

$- 2 \sqrt{10} \cdot (3 \sqrt{2^{2} \cdot 5})$

$- 2 \sqrt{10} \cdot (3 \sqrt{2^{2} \cdot 5})$

Step 2

Pull terms out from under the radical.

$- 2 \sqrt{10} \cdot (3 (2 \sqrt{5}))$

Step 3

Multiply $2$ by $3$ .

$- 2 \sqrt{10} \cdot (6 \sqrt{5})$

Step 4

Multiply $- 2 \sqrt{10} (6 \sqrt{5})$ .

Multiply $6$ by $- 2$ .

$- 12 \sqrt{10} \sqrt{5}$

Combine using the product rule for radicals.

$- 12 \sqrt{5 \cdot 10}$

Multiply $5$ by $10$ .

$- 12 \sqrt{50}$

$- 12 \sqrt{50}$

Step 5

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$- 12 \sqrt{25 (2)}$

Rewrite $25$ as $5^{2}$ .

$- 12 \sqrt{5^{2} \cdot 2}$

$- 12 \sqrt{5^{2} \cdot 2}$

Step 6

Pull terms out from under the radical.

$- 12 (5 \sqrt{2})$

Step 7

Multiply $5$ by $- 12$ .

$- 60 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- 60 \sqrt{2}$

Decimal Form:

$- 84.85281374 \dots$

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