Surds-Irrational Numbers

If ‘a’ is a rational number and ‘n’ is a positive integer such that the nth root of ‘a’ is an irrational number, then a1/n is called a surd e.g.,  Ö5,Ö3, Ö2 etc.

If  a1/n  is a surd then ‘n’ is known as order of surd and ‘a’ is known as radicand.

Every surd is an irrational number but every irrational number is not a surd.


Rational Indices:

a × a × a ……. m factors = am

Here, ‘a’ is called the base and m is called the index or power or exponent of ‘a’.


Law of Indices:

First Law: am × an = am+n This is called product law.

Second Law: am/an = am-n. This is called quotient law.

Third Law: (am)n = amn. This is called power law.

Negative Index: a-m = 1/am where, a¹ 0

Fourth Law: (ab)m = am × b m

Fifth Law: (a/b)m = am/bm

fractional index