Basic Math Examples

$(\sqrt{5} - 1) (\sqrt{3} + \sqrt{2})$

Step 1

Expand $(\sqrt{5} - 1) (\sqrt{3} + \sqrt{2})$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$\sqrt{5} (\sqrt{3} + \sqrt{2}) - 1 (\sqrt{3} + \sqrt{2})$

Step 1.2

Apply the distributive property.

$\sqrt{5} \sqrt{3} + \sqrt{5} \sqrt{2} - 1 (\sqrt{3} + \sqrt{2})$

Step 1.3

Apply the distributive property.

$\sqrt{5} \sqrt{3} + \sqrt{5} \sqrt{2} - 1 \sqrt{3} - 1 \sqrt{2}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Combine using the product rule for radicals.

$\sqrt{5 \cdot 3} + \sqrt{5} \sqrt{2} - 1 \sqrt{3} - 1 \sqrt{2}$

Step 2.2

Multiply $5$ by $3$ .

$\sqrt{15} + \sqrt{5} \sqrt{2} - 1 \sqrt{3} - 1 \sqrt{2}$

Step 2.3

Combine using the product rule for radicals.

$\sqrt{15} + \sqrt{5 \cdot 2} - 1 \sqrt{3} - 1 \sqrt{2}$

Step 2.4

Multiply $5$ by $2$ .

$\sqrt{15} + \sqrt{10} - 1 \sqrt{3} - 1 \sqrt{2}$

Step 2.5

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

$\sqrt{15} + \sqrt{10} - \sqrt{3} - 1 \sqrt{2}$

Step 2.6

Rewrite $- 1 \sqrt{2}$ as $- \sqrt{2}$ .

$\sqrt{15} + \sqrt{10} - \sqrt{3} - \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{15} + \sqrt{10} - \sqrt{3} - \sqrt{2}$

Decimal Form:

$3.88899663 \dots$