# How do you simplify ( 7 - sqrt7)/(10 +sqrt3)?

Dec 8, 2017

There is not much you can do. Only put square root to the top.

#### Explanation:

(7−√7)/(10+√3)*(10-sqrt(3))/(10-sqrt(3))=

$= \frac{70 - 10 \sqrt{7} + \sqrt{21} - 7 \sqrt{3}}{{10}^{2} - {\left(\sqrt{3}\right)}^{2}} =$

$= \frac{70 - 10 \sqrt{7} + \sqrt{21} - 7 \sqrt{3}}{97}$

Dec 8, 2017

$= \frac{70 - 7 \sqrt{3} - 10 \sqrt{7} + \sqrt{21}}{97}$

#### Explanation:

To simplify this expression we rationalise the denominator. That is multiply top and bottom by a term that will remove the square root.

We make use of the difference of squares identity

${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

$\frac{7 - \sqrt{7}}{10 + \sqrt{3}} = \frac{7 - \sqrt{7}}{10 + \sqrt{3}} \times \frac{10 - \sqrt{3}}{10 - \sqrt{3}}$

$= \frac{70 - 7 \sqrt{3} - 10 \sqrt{7} + \sqrt{21}}{100 - 3}$

$= \frac{70 - 7 \sqrt{3} - 10 \sqrt{7} + \sqrt{21}}{97}$