Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $36$ out of $108$ .

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

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Multiply $6$ by $3$ .

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

Step 1.4

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

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Step 1.4.1

Factor $9$ out of $18$ .

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

Step 1.4.2

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

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

Multiply $3$ by $- 2$ .

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

Step 1.7

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

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Step 1.7.1

Factor $16$ out of $48$ .

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

Step 1.7.2

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

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

Step 1.8

Pull terms out from under the radical.

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

Step 1.9

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:

$1.90702347 \dots$