Simplify square root of 9( square root of 3+2 square root of 2)

$\sqrt{9} (\sqrt{3} + 2 \sqrt{2})$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2}} (\sqrt{3} + 2 \sqrt{2})$

Pull terms out from under the radical, assuming positive real numbers.

$3 (\sqrt{3} + 2 \sqrt{2})$

Apply the distributive property.

$3 \sqrt{3} + 3 (2 \sqrt{2})$

Multiply $2$ by $3$ .

$3 \sqrt{3} + 6 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{3} + 6 \sqrt{2}$

Decimal Form:

$13.68143379 \dots$