Finite Math Examples

$(2 + \sqrt{3}) (2 + \sqrt{13})$

Step 1

Expand $(2 + \sqrt{3}) (2 + \sqrt{13})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 (2 + \sqrt{13}) + \sqrt{3} (2 + \sqrt{13})$

Step 1.2

Apply the distributive property.

$2 \cdot 2 + 2 \sqrt{13} + \sqrt{3} (2 + \sqrt{13})$

Step 1.3

Apply the distributive property.

$2 \cdot 2 + 2 \sqrt{13} + \sqrt{3} \cdot 2 + \sqrt{3} \sqrt{13}$

Step 2

Simplify each term.

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Step 2.1

Multiply $2$ by $2$ .

$4 + 2 \sqrt{13} + \sqrt{3} \cdot 2 + \sqrt{3} \sqrt{13}$

Step 2.2

Move $2$ to the left of $\sqrt{3}$ .

$4 + 2 \sqrt{13} + 2 \cdot \sqrt{3} + \sqrt{3} \sqrt{13}$

Step 2.3

Combine using the product rule for radicals.

$4 + 2 \sqrt{13} + 2 \sqrt{3} + \sqrt{3 \cdot 13}$

Step 2.4

Multiply $3$ by $13$ .

$4 + 2 \sqrt{13} + 2 \sqrt{3} + \sqrt{39}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 + 2 \sqrt{13} + 2 \sqrt{3} + \sqrt{39}$

Decimal Form:

$20.92020216 \dots$