Indices & Surds

Indices & Surds

Indices

Let a be a real number and m is a positive integer, then
 

Rules of Indices

Let a and b be two real number and m & n are two positive integers, then
 

Surds

Let a be rational number and n be a positive integer such that a(1/n) = a. Then, a is called a surd of order n. 
In simple terms, When we can't simplify a number to remove a square root (or cube root etc) then it is a surd.
 
Example:
  • √2 (square root of 2) can't be simplified further so it is a surd
  • √4 (square root of 4) can be simplified (to 2), so it is not a surd!
 

Comparing Magnitudes of Surds

For comparing surds convert each of them into forms having same order and then compare their bases.
 

Rules of Surds

Let a be a rational number and m & n be two integers, then 
 

Addition and Subtraction of Surds

Similiar surds can be added and subtracted but dissimilar surds cannot be added.
 

Multiplication of Surds

 

Division of Surds

 

Rationalisation

When two surds are such that their product is a rational number, either of them is called rationalising factor of the other.