Basic Math Examples

$(\sqrt{3} - \sqrt{7}) (\sqrt{11} - \sqrt{10})$

Step 1

Expand $(\sqrt{3} - \sqrt{7}) (\sqrt{11} - \sqrt{10})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{3} (\sqrt{11} - \sqrt{10}) - \sqrt{7} (\sqrt{11} - \sqrt{10})$

Step 1.2

Apply the distributive property.

$\sqrt{3} \sqrt{11} + \sqrt{3} (- \sqrt{10}) - \sqrt{7} (\sqrt{11} - \sqrt{10})$

Step 1.3

Apply the distributive property.

$\sqrt{3} \sqrt{11} + \sqrt{3} (- \sqrt{10}) - \sqrt{7} \sqrt{11} - \sqrt{7} (- \sqrt{10})$

Step 2

Simplify each term.

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Step 2.1

Combine using the product rule for radicals.

$\sqrt{3 \cdot 11} + \sqrt{3} (- \sqrt{10}) - \sqrt{7} \sqrt{11} - \sqrt{7} (- \sqrt{10})$

Step 2.2

Multiply $3$ by $11$ .

$\sqrt{33} + \sqrt{3} (- \sqrt{10}) - \sqrt{7} \sqrt{11} - \sqrt{7} (- \sqrt{10})$

Step 2.3

Multiply $\sqrt{3} (- \sqrt{10})$ .

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Step 2.3.1

Combine using the product rule for radicals.

$\sqrt{33} - \sqrt{3 \cdot 10} - \sqrt{7} \sqrt{11} - \sqrt{7} (- \sqrt{10})$

Step 2.3.2

Multiply $3$ by $10$ .

$\sqrt{33} - \sqrt{30} - \sqrt{7} \sqrt{11} - \sqrt{7} (- \sqrt{10})$

Step 2.4

Multiply $- \sqrt{7} \sqrt{11}$ .

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Step 2.4.1

Combine using the product rule for radicals.

$\sqrt{33} - \sqrt{30} - \sqrt{11 \cdot 7} - \sqrt{7} (- \sqrt{10})$

Step 2.4.2

Multiply $11$ by $7$ .

$\sqrt{33} - \sqrt{30} - \sqrt{77} - \sqrt{7} (- \sqrt{10})$

Step 2.5

Multiply $- \sqrt{7} (- \sqrt{10})$ .

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Step 2.5.1

Multiply $- 1$ by $- 1$ .

$\sqrt{33} - \sqrt{30} - \sqrt{77} + 1 \sqrt{7} \sqrt{10}$

Step 2.5.2

Multiply $\sqrt{7}$ by $1$ .

$\sqrt{33} - \sqrt{30} - \sqrt{77} + \sqrt{7} \sqrt{10}$

Step 2.5.3

Combine using the product rule for radicals.

$\sqrt{33} - \sqrt{30} - \sqrt{77} + \sqrt{7 \cdot 10}$

Step 2.5.4

Multiply $7$ by $10$ .

$\sqrt{33} - \sqrt{30} - \sqrt{77} + \sqrt{70}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{33} - \sqrt{30} - \sqrt{77} + \sqrt{70}$

Decimal Form:

$- 0.14102705 \dots$