Basic Math Examples

$(3 \sqrt{2} + 4) (5 + 4 \sqrt{6})$

Step 1

Expand $(3 \sqrt{2} + 4) (5 + 4 \sqrt{6})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 \sqrt{2} (5 + 4 \sqrt{6}) + 4 (5 + 4 \sqrt{6})$

Step 1.2

Apply the distributive property.

$3 \sqrt{2} \cdot 5 + 3 \sqrt{2} (4 \sqrt{6}) + 4 (5 + 4 \sqrt{6})$

Step 1.3

Apply the distributive property.

$3 \sqrt{2} \cdot 5 + 3 \sqrt{2} (4 \sqrt{6}) + 4 \cdot 5 + 4 (4 \sqrt{6})$

Step 2

Simplify each term.

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Step 2.1

Multiply $5$ by $3$ .

$15 \sqrt{2} + 3 \sqrt{2} (4 \sqrt{6}) + 4 \cdot 5 + 4 (4 \sqrt{6})$

Step 2.2

Multiply $3 \sqrt{2} (4 \sqrt{6})$ .

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Step 2.2.1

Multiply $4$ by $3$ .

$15 \sqrt{2} + 12 \sqrt{2} \sqrt{6} + 4 \cdot 5 + 4 (4 \sqrt{6})$

Step 2.2.2

Combine using the product rule for radicals.

$15 \sqrt{2} + 12 \sqrt{6 \cdot 2} + 4 \cdot 5 + 4 (4 \sqrt{6})$

Step 2.2.3

Multiply $6$ by $2$ .

$15 \sqrt{2} + 12 \sqrt{12} + 4 \cdot 5 + 4 (4 \sqrt{6})$

Step 2.3

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 2.3.1

Factor $4$ out of $12$ .

$15 \sqrt{2} + 12 \sqrt{4 (3)} + 4 \cdot 5 + 4 (4 \sqrt{6})$

Step 2.3.2

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

$15 \sqrt{2} + 12 \sqrt{2^{2} \cdot 3} + 4 \cdot 5 + 4 (4 \sqrt{6})$

Step 2.4

Pull terms out from under the radical.

$15 \sqrt{2} + 12 (2 \sqrt{3}) + 4 \cdot 5 + 4 (4 \sqrt{6})$

Step 2.5

Multiply $2$ by $12$ .

$15 \sqrt{2} + 24 \sqrt{3} + 4 \cdot 5 + 4 (4 \sqrt{6})$

Step 2.6

Multiply $4$ by $5$ .

$15 \sqrt{2} + 24 \sqrt{3} + 20 + 4 (4 \sqrt{6})$

Step 2.7

Multiply $4$ by $4$ .

$15 \sqrt{2} + 24 \sqrt{3} + 20 + 16 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt{2} + 24 \sqrt{3} + 20 + 16 \sqrt{6}$

Decimal Form:

$121.97425870 \dots$