Basic Math Examples

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

Step 1

Apply the distributive property.

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

Step 2

Multiply $\sqrt{2} (3 \sqrt{6})$ .

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Step 2.1

Combine using the product rule for radicals.

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

Step 2.2

Multiply $2$ by $6$ .

$2 \cdot (3 \sqrt{12} + \sqrt{2} (4 \sqrt{3}))$

Step 3

Multiply $\sqrt{2} (4 \sqrt{3})$ .

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Step 3.1

Combine using the product rule for radicals.

$2 \cdot (3 \sqrt{12} + 4 \sqrt{2 \cdot 3})$

Step 3.2

Multiply $2$ by $3$ .

$2 \cdot (3 \sqrt{12} + 4 \sqrt{6})$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Factor $4$ out of $12$ .

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

Step 4.1.2

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

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

Step 4.2

Pull terms out from under the radical.

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

Step 4.3

Multiply $2$ by $3$ .

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

Step 5

Simplify by multiplying through.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply.

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Step 5.2.1

Multiply $6$ by $2$ .

$12 \sqrt{3} + 2 (4 \sqrt{6})$

Step 5.2.2

Multiply $4$ by $2$ .

$12 \sqrt{3} + 8 \sqrt{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{3} + 8 \sqrt{6}$

Decimal Form:

$40.38052763 \dots$