Simplify 4 square root of 12- square root of 3+4 square root of 6+3 square root of 4

$4 \sqrt{12} - \sqrt{3} + 4 \sqrt{6} + 3 \sqrt{4}$

Step 1

Simplify each term.

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$4 \sqrt{4 (3)} - \sqrt{3} + 4 \sqrt{6} + 3 \sqrt{4}$

Rewrite $4$ as $2^{2}$ .

$4 \sqrt{2^{2} \cdot 3} - \sqrt{3} + 4 \sqrt{6} + 3 \sqrt{4}$

Pull terms out from under the radical.

$4 (2 \sqrt{3}) - \sqrt{3} + 4 \sqrt{6} + 3 \sqrt{4}$

Multiply $2$ by $4$ .

$8 \sqrt{3} - \sqrt{3} + 4 \sqrt{6} + 3 \sqrt{4}$

Rewrite $4$ as $2^{2}$ .

$8 \sqrt{3} - \sqrt{3} + 4 \sqrt{6} + 3 \sqrt{2^{2}}$

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

$8 \sqrt{3} - \sqrt{3} + 4 \sqrt{6} + 3 \cdot 2$

Multiply $3$ by $2$ .

$8 \sqrt{3} - \sqrt{3} + 4 \sqrt{6} + 6$

Step 2

Subtract $\sqrt{3}$ from $8 \sqrt{3}$ .

$7 \sqrt{3} + 4 \sqrt{6} + 6$

Step 3

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{3} + 4 \sqrt{6} + 6$

Decimal Form:

$27.92231462 \dots$