Basic Math Examples

$\frac{4}{7 - \sqrt{10}}$

Step 1

Multiply

$\frac{4}{7 - \sqrt{10}}$ by

$\frac{7 + \sqrt{10}}{7 + \sqrt{10}}$ .

$\frac{4}{7 - \sqrt{10}} \cdot \frac{7 + \sqrt{10}}{7 + \sqrt{10}}$

Step 2

Multiply

$\frac{4}{7 - \sqrt{10}}$ by

$\frac{7 + \sqrt{10}}{7 + \sqrt{10}}$ .

$\frac{4 (7 + \sqrt{10})}{(7 - \sqrt{10}) (7 + \sqrt{10})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (7 + \sqrt{10})}{49 + 7 \sqrt{10} - 7 \sqrt{10} - {\sqrt{10}}^{2}}$

Step 4

Simplify.

$\frac{4 (7 + \sqrt{10})}{39}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4 (7 + \sqrt{10})}{39}$

Decimal Form:

$1.04228488 \dots$