Multiply (2+3 square root of 10)(4 square root of 2-5)

$(2 + 3 \sqrt{10}) (4 \sqrt{2} - 5)$

Expand $(2 + 3 \sqrt{10}) (4 \sqrt{2} - 5)$ using the FOIL Method.

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Apply the distributive property.

$2 (4 \sqrt{2} - 5) + 3 \sqrt{10} (4 \sqrt{2} - 5)$

Apply the distributive property.

$2 (4 \sqrt{2}) + 2 \cdot - 5 + 3 \sqrt{10} (4 \sqrt{2} - 5)$

Apply the distributive property.

$2 (4 \sqrt{2}) + 2 \cdot - 5 + 3 \sqrt{10} (4 \sqrt{2}) + 3 \sqrt{10} \cdot - 5$

Simplify each term.

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Multiply $4$ by $2$ .

$8 \sqrt{2} + 2 \cdot - 5 + 3 \sqrt{10} (4 \sqrt{2}) + 3 \sqrt{10} \cdot - 5$

Multiply $2$ by $- 5$ .

$8 \sqrt{2} - 10 + 3 \sqrt{10} (4 \sqrt{2}) + 3 \sqrt{10} \cdot - 5$

Multiply $3 \sqrt{10} (4 \sqrt{2})$ .

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Multiply $4$ by $3$ .

$8 \sqrt{2} - 10 + 12 \sqrt{10} \sqrt{2} + 3 \sqrt{10} \cdot - 5$

Combine using the product rule for radicals.

$8 \sqrt{2} - 10 + 12 \sqrt{2 \cdot 10} + 3 \sqrt{10} \cdot - 5$

Multiply $2$ by $10$ .

$8 \sqrt{2} - 10 + 12 \sqrt{20} + 3 \sqrt{10} \cdot - 5$

Rewrite $20$ as $2^{2} \cdot 5$ .

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Factor $4$ out of $20$ .

$8 \sqrt{2} - 10 + 12 \sqrt{4 (5)} + 3 \sqrt{10} \cdot - 5$

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

$8 \sqrt{2} - 10 + 12 \sqrt{2^{2} \cdot 5} + 3 \sqrt{10} \cdot - 5$

Pull terms out from under the radical.

$8 \sqrt{2} - 10 + 12 (2 \sqrt{5}) + 3 \sqrt{10} \cdot - 5$

Multiply $2$ by $12$ .

$8 \sqrt{2} - 10 + 24 \sqrt{5} + 3 \sqrt{10} \cdot - 5$

Multiply $- 5$ by $3$ .

$8 \sqrt{2} - 10 + 24 \sqrt{5} - 15 \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{2} - 10 + 24 \sqrt{5} - 15 \sqrt{10}$

Decimal Form:

$7.54517505 \dots$

Multiply (2+3 square root of 10)(4 square root of 2-5)

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