# OPERATION OF SURDS

## Number system of Class 9

### ADDITION AND SUBTRACTION OF SURDS:

Addition and subtraction of surds are possible only when order and radicand are same i.e. only for surds.

question Simplify

(i) [Bring surd in simples form]

= = (15 - 6 + 4 ) = Ans.

(ii)    Ans.

(iii)    = Ans.

### MULTIPLICATION AND DIVISION OF SURDS:

e.g. (i) (i) ### COMPARISON OF SURDS:

It is clear that if x > y > 0 and n > 1 is a positive integer.

e.g. Which is greater is each of the following :

(i) and (ii) and L.C.M. of 3 and 5 15. L.C.M. of 2 and 3 is 6.      so,   ### RATIONALIZATION OF SURDS

Rationalizing factor product of two surds is a rational number then each of them is called the rationalizing factor (R.F.) of the other. The process of converting a surd to a rational number by using an appropriate multiplier is known as rationalization.

Some examples:

(i) R.F. of is (ii) R.F. of .

(iii) R.F. of & vice versa .

(iv) R.F. of a is & vice versa (v) R.F. of is  which is rational.

(vi) R.F. of question Find the R.G. (rationalizing factor) of the following:

(i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) Solution: (i).  as 10 is rational number. R.F. of is Ans.

(ii). First write it’s simplest from i.e. .

Now find R.F. (i.e. R.F. of is ) R.F. of is Ans.

(iii) Simplest from of is .

R.F. of is . R.F. of is Ans.