PUMPA - THE SMART LEARNING APP

Helps you to prepare for any school test or exam

Download now on Google PlayThe 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 \(6\).