Basic Math Examples

$(9 - \sqrt{18}) (3 + \sqrt{14})$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $18$ .

$(9 - \sqrt{9 (2)}) (3 + \sqrt{14})$

Step 1.1.2

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

$(9 - \sqrt{3^{2} \cdot 2}) (3 + \sqrt{14})$

Step 1.2

Pull terms out from under the radical.

$(9 - (3 \sqrt{2})) (3 + \sqrt{14})$

Step 1.3

Multiply $3$ by $- 1$ .

$(9 - 3 \sqrt{2}) (3 + \sqrt{14})$

Step 2

Expand $(9 - 3 \sqrt{2}) (3 + \sqrt{14})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$9 (3 + \sqrt{14}) - 3 \sqrt{2} (3 + \sqrt{14})$

Step 2.2

Apply the distributive property.

$9 \cdot 3 + 9 \sqrt{14} - 3 \sqrt{2} (3 + \sqrt{14})$

Step 2.3

Apply the distributive property.

$9 \cdot 3 + 9 \sqrt{14} - 3 \sqrt{2} \cdot 3 - 3 \sqrt{2} \sqrt{14}$

Step 3

Simplify each term.

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Step 3.1

Multiply $9$ by $3$ .

$27 + 9 \sqrt{14} - 3 \sqrt{2} \cdot 3 - 3 \sqrt{2} \sqrt{14}$

Step 3.2

Multiply $3$ by $- 3$ .

$27 + 9 \sqrt{14} - 9 \sqrt{2} - 3 \sqrt{2} \sqrt{14}$

Step 3.3

Multiply $- 3 \sqrt{2} \sqrt{14}$ .

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Step 3.3.1

Combine using the product rule for radicals.

$27 + 9 \sqrt{14} - 9 \sqrt{2} - 3 \sqrt{14 \cdot 2}$

Step 3.3.2

Multiply $14$ by $2$ .

$27 + 9 \sqrt{14} - 9 \sqrt{2} - 3 \sqrt{28}$

Step 3.4

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 3.4.1

Factor $4$ out of $28$ .

$27 + 9 \sqrt{14} - 9 \sqrt{2} - 3 \sqrt{4 (7)}$

Step 3.4.2

Rewrite $4$ as $2^{2}$ .

$27 + 9 \sqrt{14} - 9 \sqrt{2} - 3 \sqrt{2^{2} \cdot 7}$

Step 3.5

Pull terms out from under the radical.

$27 + 9 \sqrt{14} - 9 \sqrt{2} - 3 (2 \sqrt{7})$

Step 3.6

Multiply $2$ by $- 3$ .

$27 + 9 \sqrt{14} - 9 \sqrt{2} - 6 \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$27 + 9 \sqrt{14} - 9 \sqrt{2} - 6 \sqrt{7}$

Decimal Form:

$32.07248655 \dots$