Basic Math Examples

$(\sqrt{5} - 10) (\sqrt{5} - 8)$

Step 1

Expand $(\sqrt{5} - 10) (\sqrt{5} - 8)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{5} (\sqrt{5} - 8) - 10 (\sqrt{5} - 8)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

$\sqrt{5} \sqrt{5} + \sqrt{5} \cdot - 8 - 10 \sqrt{5} - 10 \cdot - 8$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine using the product rule for radicals.

$\sqrt{5 \cdot 5} + \sqrt{5} \cdot - 8 - 10 \sqrt{5} - 10 \cdot - 8$

Step 2.1.2

Multiply $5$ by $5$ .

$\sqrt{25} + \sqrt{5} \cdot - 8 - 10 \sqrt{5} - 10 \cdot - 8$

Step 2.1.3

Rewrite $25$ as $5^{2}$ .

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

Step 2.1.4

Pull terms out from under the radical, assuming positive real numbers.

$5 + \sqrt{5} \cdot - 8 - 10 \sqrt{5} - 10 \cdot - 8$

Step 2.1.5

Move $- 8$ to the left of $\sqrt{5}$ .

$5 - 8 \cdot \sqrt{5} - 10 \sqrt{5} - 10 \cdot - 8$

Step 2.1.6

Multiply $- 10$ by $- 8$ .

$5 - 8 \sqrt{5} - 10 \sqrt{5} + 80$

Step 2.2

Add $5$ and $80$ .

$85 - 8 \sqrt{5} - 10 \sqrt{5}$

Step 2.3

Subtract $10 \sqrt{5}$ from $- 8 \sqrt{5}$ .

$85 - 18 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$85 - 18 \sqrt{5}$

Decimal Form:

$44.75077640 \dots$