CHAPTER 3. SURDS 3.2
Like and Unlike Surds EMBK
Two surdsm
√
a andn√
b are called like surds if m = n, otherwise they are called unlike surds. For
example
√
2 and√
3 are like surds, however√
2 and^3√
2 are unlike surds. An important thing to
realise about the surd laws we have just learnt isthat the surds in the laws are all like surds.
If we wish to use the surd laws on unlike surds, then we must first convert them into like surds. In
order to do this we usethe formula
√nam=bn√abm (3.7)to rewrite the unlike surds so that bn is the same for all the surds.
Example 1: Like and Unlike Surds
QUESTIONSimplify to like surds asfar as possible, showingall steps:^3√
3 ×^5
√
5
SOLUTIONStep 1 : Find the common root=
15 √
35 ×
15 √
53
Step 2 : Use surd Law 1