Simplify square root of 5* square root of 12* square root of 50

$\sqrt{5} \cdot \sqrt{12} \cdot \sqrt{50}$

Combine using the product rule for radicals.

$\sqrt{5 \cdot 12} \cdot \sqrt{50}$

Combine using the product rule for radicals.

$\sqrt{5 \cdot 12 \cdot 50}$

Multiply.

Multiply $5$ by $12$ .

$\sqrt{60 \cdot 50}$

Multiply $60$ by $50$ .

$\sqrt{3000}$

Rewrite $3000$ as $10^{2} \cdot 30$ .

Factor $100$ out of $3000$ .

$\sqrt{100 (30)}$

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 30}$

Pull terms out from under the radical.

$10 \sqrt{30}$

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{30}$

Decimal Form:

$54.77225575 \dots$