Simplify the Radical Expression 7/(2+ square root of 3)

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

Step 1

Multiply $\frac{7}{2 + \sqrt{3}}$ by $\frac{2 - \sqrt{3}}{2 - \sqrt{3}}$ .

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

Step 2

Multiply $\frac{7}{2 + \sqrt{3}}$ by $\frac{2 - \sqrt{3}}{2 - \sqrt{3}}$ .

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

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

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

Step 6

Apply the distributive property.

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

Step 7

Multiply $7$ by $2$ .

$14 + 7 (- \sqrt{3})$

Step 8

Multiply $- 1$ by $7$ .

$14 - 7 \sqrt{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$14 - 7 \sqrt{3}$

Decimal Form:

$1.87564434 \dots$