# How do you simplify 7/(5+sqrt3)?

##### 2 Answers
Mar 31, 2017

$= \frac{35}{22} - \frac{7 \sqrt{3}}{22}$

#### Explanation:

You must know that the conjugate of an irrational number of the type
$a + \sqrt{b}$ is given by $a - \sqrt{b}$ and that of $a - \sqrt{b}$ is given by $a + \sqrt{b}$.

$\frac{7}{5 + \sqrt{3}}$

(multiplying and dividing by conjugate of $5 + \sqrt{3}$)

$= \frac{7}{5 + \sqrt{3}} \cdot \frac{5 - \sqrt{3}}{5 - \sqrt{3}}$

$= \frac{7 \left(5 - \sqrt{3}\right)}{{5}^{2} - {\left(\sqrt{3}\right)}^{2}}$

$= \frac{7 \left(5 - \sqrt{3}\right)}{22}$
$= \frac{35}{22} - \frac{7 \sqrt{3}}{22}$

Mar 31, 2017

Rationalise the denominator by multiplying by the conjugate surd.

#### Explanation:

$\frac{7}{5 + \sqrt{3}}$ = 7/(5 + sqrt3) * (5-sqrt3)/(5-sqrt3)

= $\frac{7 \left(5 - \sqrt{3}\right)}{\left({5}^{2}\right) - {\left(\sqrt{3}\right)}^{2}}$

= $\frac{35 - 7 \sqrt{3}}{25 - 3}$

= $\frac{35 - 7 \sqrt{3}}{22}$