Simplify 2 square root of 27+ square root of 12-3 square root of 3-2 square root of 12

$2 \sqrt{27} + \sqrt{12} - 3 \sqrt{3} - 2 \sqrt{12}$

Step 1

Simplify each term.

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$2 \sqrt{9 (3)} + \sqrt{12} - 3 \sqrt{3} - 2 \sqrt{12}$

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

$2 \sqrt{3^{2} \cdot 3} + \sqrt{12} - 3 \sqrt{3} - 2 \sqrt{12}$

Pull terms out from under the radical.

$2 (3 \sqrt{3}) + \sqrt{12} - 3 \sqrt{3} - 2 \sqrt{12}$

Multiply $3$ by $2$ .

$6 \sqrt{3} + \sqrt{12} - 3 \sqrt{3} - 2 \sqrt{12}$

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

Factor $4$ out of $12$ .

$6 \sqrt{3} + \sqrt{4 (3)} - 3 \sqrt{3} - 2 \sqrt{12}$

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

$6 \sqrt{3} + \sqrt{2^{2} \cdot 3} - 3 \sqrt{3} - 2 \sqrt{12}$

Pull terms out from under the radical.

$6 \sqrt{3} + 2 \sqrt{3} - 3 \sqrt{3} - 2 \sqrt{12}$

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

Factor $4$ out of $12$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 2$ .

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

Step 2

Simplify by adding terms.

Add $6 \sqrt{3}$ and $2 \sqrt{3}$ .

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

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

$5 \sqrt{3} - 4 \sqrt{3}$

Subtract $4 \sqrt{3}$ from $5 \sqrt{3}$ .

$\sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$