Basic Math Examples

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

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

Step 1

Multiply

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

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

\frac{\sqrt{3} - 4}{\sqrt{3} - 4}

$\frac{\sqrt{3} - 4}{\sqrt{3} - 4}$ .

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

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

\frac{\sqrt{3} - 4}{\sqrt{3} - 4}

$\frac{\sqrt{3} - 4}{\sqrt{3} - 4}$ .

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

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

Step 4

Simplify.

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

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

Step 5

Group

\sqrt{3} - 4

$\sqrt{3} - 4$ and

\sqrt{2}

$\sqrt{2}$ together.

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

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

Step 6

Apply the distributive property.

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

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

Step 7

Combine using the product rule for radicals.

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

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

Step 8

Multiply

3

$3$ by

2

$2$ .

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

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

Step 9

Move the negative in front of the fraction.

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

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

Step 10

Apply the distributive property.

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

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

Step 11

Multiply

- 4

$- 4$ by

4

$4$ .

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

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

Step 12

Split the fraction

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

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

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

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

Step 13

Move the negative in front of the fraction.

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

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

Step 14

The result can be shown in multiple forms.

Exact Form:

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

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

Decimal Form:

0.98688138 \dots

$0.98688138 \dots$