Simplify 5/(2+ square root of 3)

$\frac{5}{2 + \sqrt{3}}$

Step 1

Multiply $\frac{5}{2 + \sqrt{3}}$ by $\frac{2 - \sqrt{3}}{2 - \sqrt{3}}$ .

$\frac{5}{2 + \sqrt{3}} \cdot \frac{2 - \sqrt{3}}{2 - \sqrt{3}}$

Step 2

Multiply $\frac{5}{2 + \sqrt{3}}$ by $\frac{2 - \sqrt{3}}{2 - \sqrt{3}}$ .

$\frac{5 (2 - \sqrt{3})}{(2 + \sqrt{3}) (2 - \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (2 - \sqrt{3})}{4 - 2 \sqrt{3} + \sqrt{3} \cdot 2 - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{5 (2 - \sqrt{3})}{1}$

Step 5

Divide $5 (2 - \sqrt{3})$ by $1$ .

$5 (2 - \sqrt{3})$

Step 6

Apply the distributive property.

$5 \cdot 2 + 5 (- \sqrt{3})$

Step 7

Multiply.

Multiply $5$ by $2$ .

$10 + 5 (- \sqrt{3})$

Multiply $- 1$ by $5$ .

$10 - 5 \sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$10 - 5 \sqrt{3}$

Decimal Form:

$1.33974596 \dots$