Basic Math Examples

$(7 + \sqrt{5}) (3 - \sqrt{2})$

Step 1

Expand $(7 + \sqrt{5}) (3 - \sqrt{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 (3 - \sqrt{2}) + \sqrt{5} (3 - \sqrt{2})$

Step 1.2

Apply the distributive property.

$7 \cdot 3 + 7 (- \sqrt{2}) + \sqrt{5} (3 - \sqrt{2})$

Step 1.3

Apply the distributive property.

$7 \cdot 3 + 7 (- \sqrt{2}) + \sqrt{5} \cdot 3 + \sqrt{5} (- \sqrt{2})$

Step 2

Simplify each term.

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Step 2.1

Multiply $7$ by $3$ .

$21 + 7 (- \sqrt{2}) + \sqrt{5} \cdot 3 + \sqrt{5} (- \sqrt{2})$

Step 2.2

Multiply $- 1$ by $7$ .

$21 - 7 \sqrt{2} + \sqrt{5} \cdot 3 + \sqrt{5} (- \sqrt{2})$

Step 2.3

Move $3$ to the left of $\sqrt{5}$ .

$21 - 7 \sqrt{2} + 3 \cdot \sqrt{5} + \sqrt{5} (- \sqrt{2})$

Step 2.4

Multiply $\sqrt{5} (- \sqrt{2})$ .

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Step 2.4.1

Combine using the product rule for radicals.

$21 - 7 \sqrt{2} + 3 \sqrt{5} - \sqrt{5 \cdot 2}$

Step 2.4.2

Multiply $5$ by $2$ .

$21 - 7 \sqrt{2} + 3 \sqrt{5} - \sqrt{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$21 - 7 \sqrt{2} + 3 \sqrt{5} - \sqrt{10}$

Decimal Form:

$14.64643133 \dots$