root 2/root 5 +root 3 rationalize. Created by mamahodiombath. Math

EXPLANATION.As we know that,Rationalizes the equation, we get.

root 5 +root 3 rationalize...

As we know that,

Rationalizes the equation, we get.

$\sf \implies \displaystyle \dfrac{\sqrt{2} }{\sqrt{5} + \sqrt{3} } \times \dfrac{\sqrt{5} - \sqrt{3} }{\sqrt{5}- \sqrt{3} }$

$\sf \implies \displaystyle \dfrac{\sqrt{2} [\sqrt{5} - \sqrt{3}] }{[(\sqrt{5})^{2} - (\sqrt{3})^{2} ]}$

$\sf \implies \displaystyle \dfrac{\sqrt{10} - \sqrt{6} }{5 - 3}$

$\sf \implies \displaystyle \dfrac{\sqrt{2} }{\sqrt{5} + \sqrt{3} } = \displaystyle \dfrac{\sqrt{10} - \sqrt{6} }{2}$

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

$\frac{ \sqrt{2} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5 } - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ \\$
we know thAt formula of

$\frac{ \sqrt{2}( \sqrt{5} - \sqrt{3}) }{( \sqrt{5}) {}^{2} - (\sqrt{3}) {}^{2} } \\ \\ \frac{ \sqrt{10} - \sqrt{6} }{5 - 3} \\ \\ \frac{ \sqrt{10} - \sqrt{6} }{2}$
==================================