Basic Math Examples

$(4 - \sqrt{13}) (9 + \sqrt{3})$

Step 1

Expand $(4 - \sqrt{13}) (9 + \sqrt{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 (9 + \sqrt{3}) - \sqrt{13} (9 + \sqrt{3})$

Step 1.2

Apply the distributive property.

$4 \cdot 9 + 4 \sqrt{3} - \sqrt{13} (9 + \sqrt{3})$

Step 1.3

Apply the distributive property.

$4 \cdot 9 + 4 \sqrt{3} - \sqrt{13} \cdot 9 - \sqrt{13} \sqrt{3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $4$ by $9$ .

$36 + 4 \sqrt{3} - \sqrt{13} \cdot 9 - \sqrt{13} \sqrt{3}$

Step 2.2

Multiply $9$ by $- 1$ .

$36 + 4 \sqrt{3} - 9 \sqrt{13} - \sqrt{13} \sqrt{3}$

Step 2.3

Multiply $- \sqrt{13} \sqrt{3}$ .

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Step 2.3.1

Combine using the product rule for radicals.

$36 + 4 \sqrt{3} - 9 \sqrt{13} - \sqrt{3 \cdot 13}$

Step 2.3.2

Multiply $3$ by $13$ .

$36 + 4 \sqrt{3} - 9 \sqrt{13} - \sqrt{39}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$36 + 4 \sqrt{3} - 9 \sqrt{13} - \sqrt{39}$

Decimal Form:

$4.23324375 \dots$