Simplify 5/( square root of 14-2)

$\frac{5}{\sqrt{14} - 2}$

Step 1

Multiply $\frac{5}{\sqrt{14} - 2}$ by $\frac{\sqrt{14} + 2}{\sqrt{14} + 2}$ .

$\frac{5}{\sqrt{14} - 2} \cdot \frac{\sqrt{14} + 2}{\sqrt{14} + 2}$

Step 2

Multiply $\frac{5}{\sqrt{14} - 2}$ by $\frac{\sqrt{14} + 2}{\sqrt{14} + 2}$ .

$\frac{5 (\sqrt{14} + 2)}{(\sqrt{14} - 2) (\sqrt{14} + 2)}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (\sqrt{14} + 2)}{{\sqrt{14}}^{2} + \sqrt{14} \cdot 2 - 2 \sqrt{14} - 4}$

Step 4

Simplify.

$\frac{5 (\sqrt{14} + 2)}{10}$

Step 5

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 (\sqrt{14} + 2)}{5 \cdot 2}$

Cancel the common factor.

$\frac{5 (\sqrt{14} + 2)}{5 \cdot 2}$

Rewrite the expression.

$\frac{\sqrt{14} + 2}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{14} + 2}{2}$

Decimal Form:

$2.87082869 \dots$