Basic Math Examples

$\frac{4 \sqrt{2}}{\sqrt{3} + 4}$

Step 1

Multiply $\frac{4 \sqrt{2}}{\sqrt{3} + 4}$ by $\frac{\sqrt{3} - 4}{\sqrt{3} - 4}$ .

$\frac{4 \sqrt{2}}{\sqrt{3} + 4} \cdot \frac{\sqrt{3} - 4}{\sqrt{3} - 4}$

Step 2

Multiply $\frac{4 \sqrt{2}}{\sqrt{3} + 4}$ by $\frac{\sqrt{3} - 4}{\sqrt{3} - 4}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{4 \sqrt{2} (\sqrt{3} - 4)}{{\sqrt{3}}^{2} + \sqrt{3} \cdot - 4 + 4 \sqrt{3} - 16}$

Step 4

Simplify.

$\frac{4 \sqrt{2} (\sqrt{3} - 4)}{- 13}$

Step 5

Group $\sqrt{3} - 4$ and $\sqrt{2}$ together.

$\frac{4 ((\sqrt{3} - 4) \sqrt{2})}{- 13}$

Step 6

Apply the distributive property.

$\frac{4 (\sqrt{3} \sqrt{2} - 4 \sqrt{2})}{- 13}$

Step 7

Combine using the product rule for radicals.

$\frac{4 (\sqrt{3 \cdot 2} - 4 \sqrt{2})}{- 13}$

Step 8

Multiply $3$ by $2$ .

$\frac{4 (\sqrt{6} - 4 \sqrt{2})}{- 13}$

Step 9

Move the negative in front of the fraction.

$- \frac{4 (\sqrt{6} - 4 \sqrt{2})}{13}$

Step 10

Apply the distributive property.

$- \frac{4 \sqrt{6} + 4 (- 4 \sqrt{2})}{13}$

Step 11

Multiply $- 4$ by $4$ .

$- \frac{4 \sqrt{6} - 16 \sqrt{2}}{13}$

Step 12

Split the fraction $\frac{4 \sqrt{6} - 16 \sqrt{2}}{13}$ into two fractions.

$- (\frac{4 \sqrt{6}}{13} + \frac{- 16 \sqrt{2}}{13})$

Step 13

Move the negative in front of the fraction.

$- (\frac{4 \sqrt{6}}{13} - \frac{16 \sqrt{2}}{13})$

Step 14

The result can be shown in multiple forms.

Exact Form:

$- (\frac{4 \sqrt{6}}{13} - \frac{16 \sqrt{2}}{13})$

Decimal Form:

$0.98688138 \dots$