Finite Math Examples

$(10 + \sqrt{6}) (10 - \sqrt{3})$

Step 1

Expand $(10 + \sqrt{6}) (10 - \sqrt{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$10 (10 - \sqrt{3}) + \sqrt{6} (10 - \sqrt{3})$

Step 1.2

Apply the distributive property.

$10 \cdot 10 + 10 (- \sqrt{3}) + \sqrt{6} (10 - \sqrt{3})$

Step 1.3

Apply the distributive property.

$10 \cdot 10 + 10 (- \sqrt{3}) + \sqrt{6} \cdot 10 + \sqrt{6} (- \sqrt{3})$

Step 2

Simplify each term.

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Step 2.1

Multiply $10$ by $10$ .

$100 + 10 (- \sqrt{3}) + \sqrt{6} \cdot 10 + \sqrt{6} (- \sqrt{3})$

Step 2.2

Multiply $- 1$ by $10$ .

$100 - 10 \sqrt{3} + \sqrt{6} \cdot 10 + \sqrt{6} (- \sqrt{3})$

Step 2.3

Move $10$ to the left of $\sqrt{6}$ .

$100 - 10 \sqrt{3} + 10 \cdot \sqrt{6} + \sqrt{6} (- \sqrt{3})$

Step 2.4

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

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Step 2.4.1

Combine using the product rule for radicals.

$100 - 10 \sqrt{3} + 10 \sqrt{6} - \sqrt{6 \cdot 3}$

Step 2.4.2

Multiply $6$ by $3$ .

$100 - 10 \sqrt{3} + 10 \sqrt{6} - \sqrt{18}$

Step 2.5

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

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Step 2.5.1

Factor $9$ out of $18$ .

$100 - 10 \sqrt{3} + 10 \sqrt{6} - \sqrt{9 (2)}$

Step 2.5.2

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

$100 - 10 \sqrt{3} + 10 \sqrt{6} - \sqrt{3^{2} \cdot 2}$

Step 2.6

Pull terms out from under the radical.

$100 - 10 \sqrt{3} + 10 \sqrt{6} - (3 \sqrt{2})$

Step 2.7

Multiply $3$ by $- 1$ .

$100 - 10 \sqrt{3} + 10 \sqrt{6} - 3 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$100 - 10 \sqrt{3} + 10 \sqrt{6} - 3 \sqrt{2}$

Decimal Form:

$102.93174866 \dots$