Simplify 2 square root of 10*(3 square root of 12)

$2 \sqrt{10} \cdot (3 \sqrt{12})$

Step 1

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $2$ by $3$ .

$2 \sqrt{10} \cdot (6 \sqrt{3})$

Step 4

Multiply $2 \sqrt{10} (6 \sqrt{3})$ .

Multiply $6$ by $2$ .

$12 \sqrt{10} \sqrt{3}$

Combine using the product rule for radicals.

$12 \sqrt{3 \cdot 10}$

Multiply $3$ by $10$ .

$12 \sqrt{30}$

$12 \sqrt{30}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{30}$

Decimal Form:

$65.72670690 \dots$

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