Question

Rationalise 14/5 root3 - root5

Answer 1

Step-by-step explanation:

$\frac{14}{5 \sqrt{3}- \sqrt{5} } \times \frac{5 \sqrt{3}+ \sqrt{5} }{5 \sqrt{3}+ \sqrt{5} }= \frac{14(5 \sqrt{3}+ \sqrt{5)} }{ {(5 \sqrt{3)} }^{2} - { \sqrt{5} }^{2} }$

$= \frac{14(5 \sqrt{3}+ \sqrt{5} ) }{75-5}$

$=\frac{14(5 \sqrt{3}+ \sqrt{5}) }{70}$

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

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