# 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.

### Rationalisation

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