Simplify 2 square root of 5( square root of 6+2)

$2 \sqrt{5} (\sqrt{6} + 2)$

Apply the distributive property.

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

Multiply $2 \sqrt{5} \sqrt{6}$ .

Combine using the product rule for radicals.

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

Multiply $6$ by $5$ .

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

Multiply $2$ by $2$ .

$2 \sqrt{30} + 4 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{30} + 4 \sqrt{5}$

Decimal Form:

$19.89872306 \dots$