A surd is defined as irrational root of a rational number, for example \(\sqrt 2 ,\;\sqrt 3 \) etc. are surds. In other words, indices is also known as surds when the power of a number is a fraction such as \(2^{1/3}, 3^{1/2}, 13^{1/5}\) etc. 

Suppose we wish to simplify \(\sqrt {\frac{1}{4}} \), we can write it as 1/2. On the other hand, some numbers involving roots, such as \(\sqrt 3\) or \(\sqrt {17} \) cannot be expressed exactly in the form of a fraction. Any number of the form \(\sqrt[n]{a}\), which cannot be written as a fraction of two integers is called a surd. Thus we can define surd with these lines

(a) it is an irrational number

(b) it is a root of positive rational number

Note that \(\pi \) and \(e\) are not surds yet these numbers are known as irrational. Thus every surd is irrational number but converse is not true.