Multiply (8- square root of 2)(9+ square root of 5)

$(8 - \sqrt{2}) (9 + \sqrt{5})$

Expand $(8 - \sqrt{2}) (9 + \sqrt{5})$ using the FOIL Method.

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Apply the distributive property.

$8 (9 + \sqrt{5}) - \sqrt{2} (9 + \sqrt{5})$

Apply the distributive property.

$8 \cdot 9 + 8 \sqrt{5} - \sqrt{2} (9 + \sqrt{5})$

Apply the distributive property.

$8 \cdot 9 + 8 \sqrt{5} - \sqrt{2} \cdot 9 - \sqrt{2} \sqrt{5}$

Simplify each term.

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Multiply $8$ by $9$ .

$72 + 8 \sqrt{5} - \sqrt{2} \cdot 9 - \sqrt{2} \sqrt{5}$

Multiply $9$ by $- 1$ .

$72 + 8 \sqrt{5} - 9 \sqrt{2} - \sqrt{2} \sqrt{5}$

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

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Combine using the product rule for radicals.

$72 + 8 \sqrt{5} - 9 \sqrt{2} - \sqrt{5 \cdot 2}$

Multiply $5$ by $2$ .

$72 + 8 \sqrt{5} - 9 \sqrt{2} - \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$72 + 8 \sqrt{5} - 9 \sqrt{2} - \sqrt{10}$

Decimal Form:

$73.99834409 \dots$

Multiply (8- square root of 2)(9+ square root of 5)

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