Evaluate 2 square root of 18-2 square root of 12+2 square root of 18

$2 \sqrt{18} - 2 \sqrt{12} + 2 \sqrt{18}$

Step 1

Simplify each term.

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$2 \sqrt{9 (2)} - 2 \sqrt{12} + 2 \sqrt{18}$

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

$2 \sqrt{3^{2} \cdot 2} - 2 \sqrt{12} + 2 \sqrt{18}$

Pull terms out from under the radical.

$2 (3 \sqrt{2}) - 2 \sqrt{12} + 2 \sqrt{18}$

Multiply $3$ by $2$ .

$6 \sqrt{2} - 2 \sqrt{12} + 2 \sqrt{18}$

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

Factor $4$ out of $12$ .

$6 \sqrt{2} - 2 \sqrt{4 (3)} + 2 \sqrt{18}$

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

$6 \sqrt{2} - 2 \sqrt{2^{2} \cdot 3} + 2 \sqrt{18}$

Pull terms out from under the radical.

$6 \sqrt{2} - 2 (2 \sqrt{3}) + 2 \sqrt{18}$

Multiply $2$ by $- 2$ .

$6 \sqrt{2} - 4 \sqrt{3} + 2 \sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $2$ .

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

Step 2

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

$12 \sqrt{2} - 4 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{2} - 4 \sqrt{3}$

Decimal Form:

$10.04235951 \dots$