# 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.

- Vedic sutra
- CLASSIFICATION OF NUMBERS
- Representation Of Rational Number Of A Real Number Line
- RATIONALISATION OF SURDS
- Rational Exponents Of A Real Number
- IDENTIFICATION PRIME NUMBER
- Rational Number In Decimal Representation
- Properties Of Rational Number
- GEOMETRICAL REPRESENTATION OF REAL NUMBERS
- BASIC LAWS OF SURDS
- OPERATION OF SURDS
- Positive And Negative Exponents Of Real Number
- LAWS OF RATIONAL EXPONENTS
- solved question
- Exercise 1
- Exercise 2
- Exercise 3(True-False)
- Exercise 4 (Fill in the blanks)