lol, I'm even more lost now. I know how to make one equal the other by multiplying top and bottom by one so the appearance is altered,
but all of that, I'm lost in and don't know how to explain the root 101 still. sorry.

lol, I'm even more lost now. I know how to make one equal the other by multiplying top and bottom by one so the appearance is altered,
but all of that, I'm lost in and don't know how to explain the root 101 still. sorry.

$\begin{array}{rlll}\sqrt{101}-\sqrt{100}&=&\frac{1}{\sqrt{101}+\sqrt{100}}<0.05&\\\\ \sqrt{101}-\sqrt{100}&<&0.05 \qquad &\mbox{Here I just left the middle bit out}\\\\\sqrt{101}-10&<&0.05 &\mbox{Now I can just solve it as an inequality}\\\\\sqrt{101}&<&0.05+10 &\\\\\sqrt{101}&<&10.05\qquad &\mbox{But just by a tiny bit}&\\\\\end{array}$