Evaluate 4/(3- square root of 7)

$\frac{4}{3 - \sqrt{7}}$

Step 1

Multiply $\frac{4}{3 - \sqrt{7}}$ by $\frac{3 + \sqrt{7}}{3 + \sqrt{7}}$ .

$\frac{4}{3 - \sqrt{7}} \cdot \frac{3 + \sqrt{7}}{3 + \sqrt{7}}$

Step 2

Multiply $\frac{4}{3 - \sqrt{7}}$ by $\frac{3 + \sqrt{7}}{3 + \sqrt{7}}$ .

$\frac{4 (3 + \sqrt{7})}{(3 - \sqrt{7}) (3 + \sqrt{7})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{4 (3 + \sqrt{7})}{9 + 3 \sqrt{7} - 3 \sqrt{7} - {\sqrt{7}}^{2}}$

Step 4

Simplify.

$\frac{4 (3 + \sqrt{7})}{2}$

Step 5

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

Factor $2$ out of $4 (3 + \sqrt{7})$ .

$\frac{2 (2 (3 + \sqrt{7}))}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (2 (3 + \sqrt{7}))}{2 (1)}$

Cancel the common factor.

$\frac{2 (2 (3 + \sqrt{7}))}{2 \cdot 1}$

Rewrite the expression.

$\frac{2 (3 + \sqrt{7})}{1}$

Divide $2 (3 + \sqrt{7})$ by $1$ .

$2 (3 + \sqrt{7})$

Step 6

Apply the distributive property.

$2 \cdot 3 + 2 \sqrt{7}$

Step 7

Multiply $2$ by $3$ .

$6 + 2 \sqrt{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$6 + 2 \sqrt{7}$

Decimal Form:

$11.29150262 \dots$