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