# Talk:LESSON 7: INTRODUCTION TO SURDS

## Contents

With irrational numbers we are in trouble. The ONLY way to calculate $\pi\ltsup\gt2\lt/sup\gt$ is to use the decimal expansion (or expansion in other bases or through continued fractions or as infinite products). In each case, the expansion involves an infinite number of digits or terms. Try for example to show that $\cos(\pi)=1$ using the decimal expansion of $\pi$ and the Taylor series expansion of $\cos(x)$!
There is, however, one group of irrational numbers which can be handled with ease, namely quadratic surds. We can handle surds without ever writing down infinite terms or digits. We can even conclude that ${{1}\over{1+\sqrt (2)}} = \sqrt(2)-1$! Imagine establishing this if we did not know how to deal with surds!--B r sitaram 03:15, 1 May 2008 (UTC)