Finite Math Examples

$\frac{7}{4 - \sqrt{2}}$

Step 1

Multiply $\frac{7}{4 - \sqrt{2}}$ by $\frac{4 + \sqrt{2}}{4 + \sqrt{2}}$ .

$\frac{7}{4 - \sqrt{2}} \cdot \frac{4 + \sqrt{2}}{4 + \sqrt{2}}$

Step 2

Multiply $\frac{7}{4 - \sqrt{2}}$ by $\frac{4 + \sqrt{2}}{4 + \sqrt{2}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{7 (4 + \sqrt{2})}{16 + 4 \sqrt{2} - 4 \sqrt{2} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{7 (4 + \sqrt{2})}{14}$

Step 5

Cancel the common factors.

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Step 5.1

Factor $7$ out of $14$ .

$\frac{7 (4 + \sqrt{2})}{7 \cdot 2}$

Step 5.2

Cancel the common factor.

$\frac{7 (4 + \sqrt{2})}{7 \cdot 2}$

Step 5.3

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.70710678 \dots$