Well there would be a number of ways Sweatie. The easiest one is to use a calculator.
This is another way:
You know it is between 2 and 3
$$2<\sqrt{6}<3$$
$$\\2.5^2=6.25 \qquad $that is too big$\\\\
2 < \sqrt{6}<2.5\\\\
2.3^2=5.29\qquad $too small$\\\\
2.3 < \sqrt{6}<2.5\\\\
2.4^2=5.76 \qquad $too small$\\\\
2.4 < \sqrt{6}<2.5\\\\
etc$$
you can continue to do this untill you get the accuracy that you need.
Note: I did not use a calculator at all for what I have done so far there.
This is an incite into how I do it. :)
$$\\23^2=(20+3)^2=400+2*3*20+9=400+120+9=529\\
so\\
2.3^2=5.29\\
$I can do that in my head - with practice you could too. :)$$$
.
+118735 
