Question 1066672
.
<pre>
{{{1/(sqrt(100) + sqrt(102))}}} = multiply the numerator and denominator by {{{(sqrt(100) - sqrt(102))}}} (rationalizing the denominator) to get = {{{(sqrt(100) - sqrt(102))/(-2)}}}.


Do it with every atom in your long molecule.

Then add.


Everything inside will cancel.


Only two terms survive: very first and very last.


So, the sum is


{{{sqrt(100)/(-2)}}} - {{{sqrt(10000)/(-2)}}} = {{{10/(-2) - 100/(-2)}}} = -5 - (-50) = 45.
</pre>

SOLVED.