Simplify 2 square root of 30*5 square root of 60

$2 \sqrt{30} \cdot 5 \sqrt{60}$

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$2 \sqrt{30} \cdot (5 \sqrt{4 (15)})$

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

$2 \sqrt{30} \cdot (5 \sqrt{2^{2} \cdot 15})$

$2 \sqrt{30} \cdot (5 \sqrt{2^{2} \cdot 15})$

Pull terms out from under the radical.

$2 \sqrt{30} \cdot (5 (2 \sqrt{15}))$

Multiply $2$ by $5$ .

$2 \sqrt{30} \cdot (10 \sqrt{15})$

Multiply $2 \sqrt{30} (10 \sqrt{15})$ .

Multiply $10$ by $2$ .

$20 \sqrt{30} \sqrt{15}$

Combine using the product rule for radicals.

$20 \sqrt{15 \cdot 30}$

Multiply $15$ by $30$ .

$20 \sqrt{450}$

$20 \sqrt{450}$

Rewrite $450$ as $15^{2} \cdot 2$ .

Factor $225$ out of $450$ .

$20 \sqrt{225 (2)}$

Rewrite $225$ as $15^{2}$ .

$20 \sqrt{15^{2} \cdot 2}$

$20 \sqrt{15^{2} \cdot 2}$

Pull terms out from under the radical.

$20 (15 \sqrt{2})$

Multiply $15$ by $20$ .

$300 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$300 \sqrt{2}$

Decimal Form:

$424.26406871 \dots$

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