Simplify square root of 5* square root of 6* square root of 2

$\sqrt{5} \cdot \sqrt{6} \cdot \sqrt{2}$

Combine using the product rule for radicals.

$\sqrt{5 \cdot 6} \cdot \sqrt{2}$

Combine using the product rule for radicals.

$\sqrt{5 \cdot 6 \cdot 2}$

Multiply.

Multiply $5$ by $6$ .

$\sqrt{30 \cdot 2}$

Multiply $30$ by $2$ .

$\sqrt{60}$

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

Factor $4$ out of $60$ .

$\sqrt{4 (15)}$

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

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

Pull terms out from under the radical.

$2 \sqrt{15}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{15}$

Decimal Form:

$7.74596669 \dots$