Pre-Algebra Examples

$\frac{\sqrt{5}}{\sqrt{3} + 2}$

Step 1

Multiply $\frac{\sqrt{5}}{\sqrt{3} + 2}$ by $\frac{\sqrt{3} - 2}{\sqrt{3} - 2}$ .

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

Step 2

Multiply $\frac{\sqrt{5}}{\sqrt{3} + 2}$ by $\frac{\sqrt{3} - 2}{\sqrt{3} - 2}$ .

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Move the negative one from the denominator of $\frac{\sqrt{5} (\sqrt{3} - 2)}{- 1}$ .

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

Step 6

Rewrite $- 1 \cdot (\sqrt{5} (\sqrt{3} - 2))$ as $- (\sqrt{5} (\sqrt{3} - 2))$ .

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

Step 7

Apply the distributive property.

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

Step 8

Combine using the product rule for radicals.

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

Step 9

Move $- 2$ to the left of $\sqrt{5}$ .

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

Step 10

Multiply $5$ by $3$ .

$- (\sqrt{15} - 2 \sqrt{5})$

Step 11

Apply the distributive property.

$- \sqrt{15} - (- 2 \sqrt{5})$

Step 12

Multiply $- 2$ by $- 1$ .

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

Step 13

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.59915260 \dots$