Basic Math Examples

$(2 + 2 \sqrt{6}) (8 + \sqrt{3})$

Step 1

Expand $(2 + 2 \sqrt{6}) (8 + \sqrt{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 (8 + \sqrt{3}) + 2 \sqrt{6} (8 + \sqrt{3})$

Step 1.2

Apply the distributive property.

$2 \cdot 8 + 2 \sqrt{3} + 2 \sqrt{6} (8 + \sqrt{3})$

Step 1.3

Apply the distributive property.

$2 \cdot 8 + 2 \sqrt{3} + 2 \sqrt{6} \cdot 8 + 2 \sqrt{6} \sqrt{3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $2$ by $8$ .

$16 + 2 \sqrt{3} + 2 \sqrt{6} \cdot 8 + 2 \sqrt{6} \sqrt{3}$

Step 2.2

Multiply $8$ by $2$ .

$16 + 2 \sqrt{3} + 16 \sqrt{6} + 2 \sqrt{6} \sqrt{3}$

Step 2.3

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

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Step 2.3.1

Combine using the product rule for radicals.

$16 + 2 \sqrt{3} + 16 \sqrt{6} + 2 \sqrt{3 \cdot 6}$

Step 2.3.2

Multiply $3$ by $6$ .

$16 + 2 \sqrt{3} + 16 \sqrt{6} + 2 \sqrt{18}$

Step 2.4

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

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Step 2.4.1

Factor $9$ out of $18$ .

$16 + 2 \sqrt{3} + 16 \sqrt{6} + 2 \sqrt{9 (2)}$

Step 2.4.2

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

$16 + 2 \sqrt{3} + 16 \sqrt{6} + 2 \sqrt{3^{2} \cdot 2}$

Step 2.5

Pull terms out from under the radical.

$16 + 2 \sqrt{3} + 16 \sqrt{6} + 2 (3 \sqrt{2})$

Step 2.6

Multiply $3$ by $2$ .

$16 + 2 \sqrt{3} + 16 \sqrt{6} + 6 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$16 + 2 \sqrt{3} + 16 \sqrt{6} + 6 \sqrt{2}$

Decimal Form:

$67.14121887 \dots$