Editing Difference of two squares (section)

===Rationalising denominators===
The difference of two squares can also be used, in reverse, in the [[Rationalisation (mathematics)|rationalising]] of [[irrational number|irrational]] [[denominator]]s.<ref>[http://www.themathpage.com/alg/multiply-radicals.htm Multiplying Radicals] TheMathPage.com, retrieved 22 December 2011</ref> This is a method for removing [[Nth root|surds]] from expressions (or at least moving them), applying to division by some combinations involving [[square root]]s.

For example, the denominator of <math>5 \big/ \bigl(4 + \sqrt{3}\bigr)</math> can be rationalised as follows:

<math display=block>\begin{align}
\dfrac{5}{4 + \sqrt{3}}
&= \dfrac{5}{4 + \sqrt{3}} \times \dfrac{4 - \sqrt{3}}{4 - \sqrt{3}} \\[10mu]
&= \dfrac{5\bigl(4 - \sqrt{3}\bigr)}{4^2 - \sqrt{3}^2}
= \dfrac{5\bigl(4 - \sqrt{3}\bigr)}{16 - 3}
= \frac{5\bigl(4 - \sqrt{3}\bigr)}{13}.
\end{align}</math>

Here, the irrational denominator <math>4 + \sqrt{3}</math> has been rationalised to <math>13</math>.