Theory:

The root of a number which cannot be futher simplified into a whole or a rational number is called as surds. \(\sqrt[n]{a}\) is a surd where \(n \in N\), \(n > 1\), \(a\) is a rational number.
Example:
Consider \(\sqrt{3}\) and \(\sqrt[3]{4}\).
 
Here, \(\sqrt{3} = 1.732....\)
 
\(\sqrt[3]{4} = 1.587....\)
 
These terms when simplifying, we get a number whose terms are non-recurring, non-terminating decimal numbers(irrational numbers).
 
Therefore, \(\sqrt{3}\) and \(\sqrt[3]{4}\) are surds.
Order of a surd
The order of a surd is defined as the number which indicates the index of the root. That is, the order of the surd \(\sqrt[n]{x}\) is \(n\).
Example:
Find the order of the surds \(\sqrt{31}\) and \(\sqrt[6]{88}\).
 
Solution:
 
1. The index of the root \(\sqrt{31}\) is \(2\). Therefore, the order of the surd is \(2\).
 
2. The index of the root \(\sqrt[6]{88}\) is \(6\). Therefore, the order of the surd is \(6\).