Simplify 2 square root of 5(13+ square root of 2)

$2 \sqrt{5} (13 + \sqrt{2})$

Apply the distributive property.

$2 \sqrt{5} \cdot 13 + 2 \sqrt{5} \sqrt{2}$

Multiply $13$ by $2$ .

$26 \sqrt{5} + 2 \sqrt{5} \sqrt{2}$

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

Combine using the product rule for radicals.

$26 \sqrt{5} + 2 \sqrt{2 \cdot 5}$

Multiply $2$ by $5$ .

$26 \sqrt{5} + 2 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$26 \sqrt{5} + 2 \sqrt{10}$

Decimal Form:

$64.46232273 \dots$