Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $12$ .

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

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 2

Simplify terms.

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Step 2.1

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

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

Step 2.2

Apply the distributive property.

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

Step 3

Multiply $\sqrt{6} (4 \sqrt{3})$ .

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Step 3.1

Combine using the product rule for radicals.

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

Step 3.2

Multiply $6$ by $3$ .

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

Step 4

Multiply $\sqrt{6} (- \sqrt{2})$ .

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Step 4.1

Combine using the product rule for radicals.

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

Step 4.2

Multiply $6$ by $2$ .

$4 \sqrt{18} - \sqrt{12}$

Step 5

Simplify each term.

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Step 5.1

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

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Step 5.1.1

Factor $9$ out of $18$ .

$4 \sqrt{9 (2)} - \sqrt{12}$

Step 5.1.2

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

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

Step 5.2

Pull terms out from under the radical.

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

Step 5.3

Multiply $3$ by $4$ .

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

Step 5.4

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

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Step 5.4.1

Factor $4$ out of $12$ .

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

Step 5.4.2

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

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

Step 5.5

Pull terms out from under the radical.

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

Step 5.6

Multiply $2$ by $- 1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$13.50646113 \dots$