Multiply (3- square root of 7)(5+ square root of 2)

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

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

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

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Multiply $3$ by $5$ .

$15 + 3 \sqrt{2} - \sqrt{7} \cdot 5 - \sqrt{7} \sqrt{2}$

Multiply $5$ by $- 1$ .

$15 + 3 \sqrt{2} - 5 \sqrt{7} - \sqrt{7} \sqrt{2}$

Multiply $- \sqrt{7} \sqrt{2}$ .

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Combine using the product rule for radicals.

$15 + 3 \sqrt{2} - 5 \sqrt{7} - \sqrt{2 \cdot 7}$

Multiply $2$ by $7$ .

$15 + 3 \sqrt{2} - 5 \sqrt{7} - \sqrt{14}$

The result can be shown in multiple forms.

Exact Form:

$15 + 3 \sqrt{2} - 5 \sqrt{7} - \sqrt{14}$

Decimal Form:

$2.27222674 \dots$

Multiply (3- square root of 7)(5+ square root of 2)