Vikasana - CET 2012

All these number have rational number under the root sign. Sonumber under the root sign. So they are the irrational roots of a rational numbers they are called

Vikasana - CET 2012rational numbers .they are called surds.

Surd : An irrational root of aSurd : - An irrational root of a rational number is called a Surd.

Vikasana - CET 2012

Vikasana - CET 2012

always be a rational number.

Vikasana - CET 2012

Vikasana - CET 2012

Reduction of a surd

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Pure surds

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Mixed Surd 

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Like [similar] SurdLike [similar] Surd

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Unlike (dissimilar) Surds U e (d ss a ) Su ds

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Vikasana - CET 2012

Vikasana - CET 2012

Operations of SurdsOperations of Surds

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Vikasana - CET 2012

Multiplication of Surds :‐Multiplication of Surds :

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Method to convert the surds of differentMethod to convert the surds of different order to same order :‐

First take LCM of the ordersFirst take LCM of the orders of the given surdsConvert each surd into index form and express then as surds with LCM as the order.

Vikasana - CET 2012

Division of surds :-

Apply same procedure as in theApply same procedure as in the case of multiplication of surds.

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Division of surds :-

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Rationalisation :-

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RATIONALISATION:

Vikasana - CET 2012

RATIONALISATION:

Definition of rationalising factor andDefinition of rationalising factor and rationalisation:- If the product of two surds is a rational number then onesurds is a rational number, then one surd is called as the rationalising factor of another and this process isfactor of another and this process is then called rationalisation.

Vikasana - CET 2012

RATIONALISATION:S.N Surd Rationalising

Factor1

22

3

4

5 a2/3Vikasana - CET 2012

5

6 52/3

Binomial Surds :-

The sum of two surds or the sum of aThe sum of two surds or the sum of a surd and rational number is called a Binomial SurdBinomial Surd.

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Binomial Surds :-

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Conjugate surds :-j g

Vikasana - CET 2012

Vikasana - CET 2012

Example : -S N Surd Rationalising  Conjugate S.N Surd Rationalising 

FactorConjugate 

Surd11

21)

3

4 a2/3‐ a1/3 b1/3 + b2/3 ‐

/   / b /  b /

Vikasana - CET 20125 a2/3+ a1/3 b1/3+ b2/3 ‐

Vikasana - CET 2012