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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 $$6$$.