Question

Rationalisation the denominator of 2 root 5 by 5 - root 3

Answer 1

$\bold{Given,}\ \bold{\frac{2\sqrt{5} }{5-\sqrt{3}} }\\\\\bold{=\frac{2\sqrt{5}(5+\sqrt{3})}{(5-\sqrt{3})(5+\sqrt{3})} }\\\\\bold{=\frac{10\sqrt{5}+2\sqrt{15}}{(5)^2-(\sqrt{3})^2} }\\\\\bold{=\frac{10\sqrt{5}+2\sqrt{15}}{25-3} }\\\\\bold{=\frac{10\sqrt{5}+2\sqrt{15}}{22}}\\\\\bold{=\frac{2(5\sqrt{5}+\sqrt{15})}{22} }\\\\\bold{=\frac{5\sqrt{5}+\sqrt{15}}{11} }$

Hope this helps....