Question 1017549
.
How can i rationalise this surd

{{{ 1/(sqrt(2)+sqrt(3)+sqrt(5)) }}}
------------------------------------------


<pre>
{{{ 1/(sqrt(2)+sqrt(3)+sqrt(5)) }}} =        <----- Multiply the numerator and the denominator by {{{sqrt(2)+sqrt(3)-sqrt(5)}}}. You will get


= {{{ (sqrt(2)+sqrt(3)-sqrt(5)) / ( ((sqrt(2)+sqrt(3))+sqrt(5))*(sqrt(2)+sqrt(3))-sqrt(5)))}}} = {{{ (sqrt(2)+sqrt(3)-sqrt(5)) /  ((sqrt(2)+sqrt(3))^2 - (sqrt(5)^2))}}} = {{{ (sqrt(2)+sqrt(3)-sqrt(5)) /  (2 + 3 +2*sqrt(6) - 5)}}} = 

= {{{ (sqrt(2)+sqrt(3)-sqrt(5)) / (2*sqrt(6))}}} =      <----- Multiply the numerator and the denominator by {{{sqrt(6)}}}. You will get

= {{{((sqrt(2)+sqrt(3)-sqrt(5))*sqrt(6))/(2*sqrt(6)*sqrt(6))}}} = {{{(sqrt(12)+sqrt(18)-sqrt(30))/12}}} = {{{(2*sqrt(3)+3*sqrt(2)-sqrt(30))/12}}}

The problem is solved. 
</pre>