Simplify 3 square root of 32-2 square root of 18+ square root of 54

$3 \sqrt{32} - 2 \sqrt{18} + \sqrt{54}$

Simplify each term.

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$3 \sqrt{16 (2)} - 2 \sqrt{18} + \sqrt{54}$

Rewrite $16$ as $4^{2}$ .

$3 \sqrt{4^{2} \cdot 2} - 2 \sqrt{18} + \sqrt{54}$

Pull terms out from under the radical.

$3 (4 \sqrt{2}) - 2 \sqrt{18} + \sqrt{54}$

Multiply $4$ by $3$ .

$12 \sqrt{2} - 2 \sqrt{18} + \sqrt{54}$

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

Factor $9$ out of $18$ .

$12 \sqrt{2} - 2 \sqrt{9 (2)} + \sqrt{54}$

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

$12 \sqrt{2} - 2 \sqrt{3^{2} \cdot 2} + \sqrt{54}$

Pull terms out from under the radical.

$12 \sqrt{2} - 2 (3 \sqrt{2}) + \sqrt{54}$

Multiply $3$ by $- 2$ .

$12 \sqrt{2} - 6 \sqrt{2} + \sqrt{54}$

Rewrite $54$ as $3^{2} \cdot 6$ .

Factor $9$ out of $54$ .

$12 \sqrt{2} - 6 \sqrt{2} + \sqrt{9 (6)}$

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

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

Pull terms out from under the radical.

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

Subtract $6 \sqrt{2}$ from $12 \sqrt{2}$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$15.83375060 \dots$