Basic Math Examples

$(2 \sqrt{6} - 1) (3 + \sqrt{3})$

Step 1

Expand $(2 \sqrt{6} - 1) (3 + \sqrt{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 \sqrt{6} (3 + \sqrt{3}) - 1 (3 + \sqrt{3})$

Step 1.2

Apply the distributive property.

$2 \sqrt{6} \cdot 3 + 2 \sqrt{6} \sqrt{3} - 1 (3 + \sqrt{3})$

Step 1.3

Apply the distributive property.

$2 \sqrt{6} \cdot 3 + 2 \sqrt{6} \sqrt{3} - 1 \cdot 3 - 1 \sqrt{3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $3$ by $2$ .

$6 \sqrt{6} + 2 \sqrt{6} \sqrt{3} - 1 \cdot 3 - 1 \sqrt{3}$

Step 2.2

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

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Step 2.2.1

Combine using the product rule for radicals.

$6 \sqrt{6} + 2 \sqrt{3 \cdot 6} - 1 \cdot 3 - 1 \sqrt{3}$

Step 2.2.2

Multiply $3$ by $6$ .

$6 \sqrt{6} + 2 \sqrt{18} - 1 \cdot 3 - 1 \sqrt{3}$

Step 2.3

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

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Step 2.3.1

Factor $9$ out of $18$ .

$6 \sqrt{6} + 2 \sqrt{9 (2)} - 1 \cdot 3 - 1 \sqrt{3}$

Step 2.3.2

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

$6 \sqrt{6} + 2 \sqrt{3^{2} \cdot 2} - 1 \cdot 3 - 1 \sqrt{3}$

Step 2.4

Pull terms out from under the radical.

$6 \sqrt{6} + 2 (3 \sqrt{2}) - 1 \cdot 3 - 1 \sqrt{3}$

Step 2.5

Multiply $3$ by $2$ .

$6 \sqrt{6} + 6 \sqrt{2} - 1 \cdot 3 - 1 \sqrt{3}$

Step 2.6

Multiply $- 1$ by $3$ .

$6 \sqrt{6} + 6 \sqrt{2} - 3 - 1 \sqrt{3}$

Step 2.7

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$18.45016902 \dots$