OPERATION OF SURDS

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.