Simplify 7+ square root of 6(3+4)-2+9-3*2^2

$7 + \sqrt{6 (3 + 4) - 2 + 9} - 3 \cdot 2^{2}$

Simplify each term.

Add $3$ and $4$ .

$7 + \sqrt{6 \cdot 7 - 2 + 9} - 3 \cdot 2^{2}$

Multiply $6$ by $7$ .

$7 + \sqrt{42 - 2 + 9} - 3 \cdot 2^{2}$

Subtract $2$ from $42$ .

$7 + \sqrt{40 + 9} - 3 \cdot 2^{2}$

Add $40$ and $9$ .

$7 + \sqrt{49} - 3 \cdot 2^{2}$

Rewrite $49$ as $7^{2}$ .

$7 + \sqrt{7^{2}} - 3 \cdot 2^{2}$

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

$7 + 7 - 3 \cdot 2^{2}$

Raise $2$ to the power of $2$ .

$7 + 7 - 3 \cdot 4$

Multiply $- 3$ by $4$ .

$7 + 7 - 12$

Simplify by adding and subtracting.

Add $7$ and $7$ .

$14 - 12$

Subtract $12$ from $14$ .

$2$