This rule says that if the square root of any particular number is multiplied by separate constants and either the sum of difference of the expressions are calculated then the result will be the same as if the constants have been added or subtracted and then multiplied by the square root in question. This sounds quite complicated but isn’t in fact as bad as it might seem:

There are in fact a few more rules with regard to surds, these are slightly more complicated than the three you’ve already met and deal in the most part with an operation we can perform on surds called “rationalisation”. Again “rationalisation” is simply an operation we can apply to surds to make them simpler to handle, and mainly involves simply removing the surd from the denominator (there will be occasions when you will look at the results and wonder “is this any simpler?”, but in many cases it will be).

You will meet these next. Now let us move to the next rule which exemplifies this.