Basic Math Examples

\frac{12}{\sqrt{2} + 1}

$\frac{12}{\sqrt{2} + 1}$

Step 1

Multiply

\frac{12}{\sqrt{2} + 1}

$\frac{12}{\sqrt{2} + 1}$ by

\frac{\sqrt{2} - 1}{\sqrt{2} - 1}

$\frac{\sqrt{2} - 1}{\sqrt{2} - 1}$ .

\frac{12}{\sqrt{2} + 1} \cdot \frac{\sqrt{2} - 1}{\sqrt{2} - 1}

$\frac{12}{\sqrt{2} + 1} \cdot \frac{\sqrt{2} - 1}{\sqrt{2} - 1}$

Step 2

Multiply

\frac{12}{\sqrt{2} + 1}

$\frac{12}{\sqrt{2} + 1}$ by

\frac{\sqrt{2} - 1}{\sqrt{2} - 1}

$\frac{\sqrt{2} - 1}{\sqrt{2} - 1}$ .

\frac{12 (\sqrt{2} - 1)}{(\sqrt{2} + 1) (\sqrt{2} - 1)}

$\frac{12 (\sqrt{2} - 1)}{(\sqrt{2} + 1) (\sqrt{2} - 1)}$

Step 3

Expand the denominator using the FOIL method.

\frac{12 (\sqrt{2} - 1)}{{\sqrt{2}}^{2} + \sqrt{2} \cdot - 1 + \sqrt{2} - 1}

$\frac{12 (\sqrt{2} - 1)}{{\sqrt{2}}^{2} + \sqrt{2} \cdot - 1 + \sqrt{2} - 1}$

Step 4

Simplify.

\frac{12 (\sqrt{2} - 1)}{1}

$\frac{12 (\sqrt{2} - 1)}{1}$

Step 5

Divide

12 (\sqrt{2} - 1)

$12 (\sqrt{2} - 1)$ by

1

$1$ .

12 (\sqrt{2} - 1)

$12 (\sqrt{2} - 1)$

Step 6

Apply the distributive property.

12 \sqrt{2} + 12 \cdot - 1

$12 \sqrt{2} + 12 \cdot - 1$

Step 7

Multiply

12

$12$ by

- 1

$- 1$ .

12 \sqrt{2} - 12

$12 \sqrt{2} - 12$

Step 8

The result can be shown in multiple forms.

Exact Form:

12 \sqrt{2} - 12

$12 \sqrt{2} - 12$

Decimal Form:

4.97056274 \dots

$4.97056274 \dots$