A surd which has unity as its rational factor, other factor being irrational is called a pure surd. For example \(\sqrt {13} ,\;\sqrt {15} \;,\sqrt[4]{{27}}\) are pure surds.

A surd having rational factor other than unity along with irrational factor is called a mixed surd.

For example \(2\sqrt 2 ,\;3\sqrt {13} \) are mixed surds.

A pure surd sometimes can be expressed as mixed surds. 

For example \(\sqrt {60}  = 2\sqrt {15} ,\;2\sqrt 2  = \sqrt 8 \) etc