Simplify ( square root of 5+7)( square root of 6+2)

$(\sqrt{5} + 7) (\sqrt{6} + 2)$

Expand $(\sqrt{5} + 7) (\sqrt{6} + 2)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{5} (\sqrt{6} + 2) + 7 (\sqrt{6} + 2)$

Apply the distributive property.

$\sqrt{5} \sqrt{6} + \sqrt{5} \cdot 2 + 7 (\sqrt{6} + 2)$

Apply the distributive property.

$\sqrt{5} \sqrt{6} + \sqrt{5} \cdot 2 + 7 \sqrt{6} + 7 \cdot 2$

Simplify each term.

Combine using the product rule for radicals.

$\sqrt{5 \cdot 6} + \sqrt{5} \cdot 2 + 7 \sqrt{6} + 7 \cdot 2$

Multiply $5$ by $6$ .

$\sqrt{30} + \sqrt{5} \cdot 2 + 7 \sqrt{6} + 7 \cdot 2$

Move $2$ to the left of $\sqrt{5}$ .

$\sqrt{30} + 2 \cdot \sqrt{5} + 7 \sqrt{6} + 7 \cdot 2$

Multiply $7$ by $2$ .

$\sqrt{30} + 2 \sqrt{5} + 7 \sqrt{6} + 14$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{30} + 2 \sqrt{5} + 7 \sqrt{6} + 14$

Decimal Form:

$41.09578972 \dots$