taylor-what?

I did a search for cloth-simulation articles, found one I liked, and implemented it. In it''s basic form I understand completely what is going on, and it works. The paper I got it from, however, says that you can avoid doing the square root (with an approximation). I don''t understand that bit, and if I use their code blindly my cloth explodes, leaving my character naked and alone http://www.ioi.dk/Homepages/thomasj/publications/gdc2001.htm If you go about half way down (a search for Taylor-expansion would do) you see the bit where he removes the sqrt. Can anyone explain it to me?