Evaluate 4/( square root of 6-2)

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

Step 1

Multiply $\frac{4}{\sqrt{6} - 2}$ by $\frac{\sqrt{6} + 2}{\sqrt{6} + 2}$ .

$\frac{4}{\sqrt{6} - 2} \cdot \frac{\sqrt{6} + 2}{\sqrt{6} + 2}$

Step 2

Multiply $\frac{4}{\sqrt{6} - 2}$ by $\frac{\sqrt{6} + 2}{\sqrt{6} + 2}$ .

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 (\sqrt{6} + 2)$ .

$\frac{2 (2 (\sqrt{6} + 2))}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (2 (\sqrt{6} + 2))}{2 (1)}$

Cancel the common factor.

$\frac{2 (2 (\sqrt{6} + 2))}{2 \cdot 1}$

Rewrite the expression.

$\frac{2 (\sqrt{6} + 2)}{1}$

Divide $2 (\sqrt{6} + 2)$ by $1$ .

$2 (\sqrt{6} + 2)$

Step 6

Apply the distributive property.

$2 \sqrt{6} + 2 \cdot 2$

Step 7

Multiply $2$ by $2$ .

$2 \sqrt{6} + 4$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{6} + 4$

Decimal Form:

$8.89897948 \dots$