Evaluate 3 square root of 108-2 square root of 18-3 square root of 48

$3 \sqrt{108} - 2 \sqrt{18} - 3 \sqrt{48}$

Step 1

Simplify each term.

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

$3 \sqrt{36 (3)} - 2 \sqrt{18} - 3 \sqrt{48}$

Rewrite $36$ as $6^{2}$ .

$3 \sqrt{6^{2} \cdot 3} - 2 \sqrt{18} - 3 \sqrt{48}$

Pull terms out from under the radical.

$3 (6 \sqrt{3}) - 2 \sqrt{18} - 3 \sqrt{48}$

Multiply $6$ by $3$ .

$18 \sqrt{3} - 2 \sqrt{18} - 3 \sqrt{48}$

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

Factor $9$ out of $18$ .

$18 \sqrt{3} - 2 \sqrt{9 (2)} - 3 \sqrt{48}$

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

$18 \sqrt{3} - 2 \sqrt{3^{2} \cdot 2} - 3 \sqrt{48}$

Pull terms out from under the radical.

$18 \sqrt{3} - 2 (3 \sqrt{2}) - 3 \sqrt{48}$

Multiply $3$ by $- 2$ .

$18 \sqrt{3} - 6 \sqrt{2} - 3 \sqrt{48}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$18 \sqrt{3} - 6 \sqrt{2} - 3 \sqrt{16 (3)}$

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

$18 \sqrt{3} - 6 \sqrt{2} - 3 \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

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

Multiply $4$ by $- 3$ .

$18 \sqrt{3} - 6 \sqrt{2} - 12 \sqrt{3}$

Step 2

Subtract $12 \sqrt{3}$ from $18 \sqrt{3}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.90702347 \dots$