Basic Math Examples

$(2 \sqrt{3} - 8 \sqrt{2}) (7 \sqrt{3 + \sqrt{2}})$

Step 1

Apply the distributive property.

$2 \sqrt{3} (7 \sqrt{3 + \sqrt{2}}) - 8 \sqrt{2} (7 \sqrt{3 + \sqrt{2}})$

Step 2

Multiply $2 \sqrt{3} (7 \sqrt{3 + \sqrt{2}})$ .

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Step 2.1

Multiply $7$ by $2$ .

$14 \sqrt{3} \sqrt{3 + \sqrt{2}} - 8 \sqrt{2} (7 \sqrt{3 + \sqrt{2}})$

Step 2.2

Combine using the product rule for radicals.

$14 \sqrt{(3 + \sqrt{2}) \cdot 3} - 8 \sqrt{2} (7 \sqrt{3 + \sqrt{2}})$

Step 3

Multiply $- 8 \sqrt{2} (7 \sqrt{3 + \sqrt{2}})$ .

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Step 3.1

Multiply $7$ by $- 8$ .

$14 \sqrt{(3 + \sqrt{2}) \cdot 3} - 56 \sqrt{2} \sqrt{3 + \sqrt{2}}$

Step 3.2

Combine using the product rule for radicals.

$14 \sqrt{(3 + \sqrt{2}) \cdot 3} - 56 \sqrt{(3 + \sqrt{2}) \cdot 2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$14 \sqrt{(3 + \sqrt{2}) \cdot 3} - 56 \sqrt{(3 + \sqrt{2}) \cdot 2}$

Decimal Form:

$- 115.44433271 \dots$