Surd Quant Notes | EduRev

Quantitative Techniques for CLAT

Created by: Gyanm Institute

Quant : Surd Quant Notes | EduRev

The document Surd Quant Notes | EduRev is a part of the Quant Course Quantitative Techniques for CLAT.
All you need of Quant at this link: Quant

SURDS

If a is a rational number and n is a positive integer such that the nth root of a i.e. a1/n or Surd Quant Notes | EduRev is an irrational number, then  a1/n is called a surd. It is also called a radical of order n, a is called the radicand.

 FOR EXAMPLE 

i)Surd Quant Notes | EduRev is a surd. It can also be written as (3)1/2, Since 3 is a rational number and 2 is a positive integer and Surd Quant Notes | EduRev is an irrational number. So Surd Quant Notes | EduRev is a surd.

 ii)Surd Quant Notes | EduRev is not a surd

Because 8 is a rational number and 3 is a +ve integer but Surd Quant Notes | EduRev  =2 is not an irrational number. So Surd Quant Notes | EduRev is not a surd

iii)Surd Quant Notes | EduRev is not a surd because  2 + Surd Quant Notes | EduRev is not a rational number.

 iv) Every surd is an irrational number but every irrational number is not a surd

 

LAWS OF SURDS. 

i) For every positive integer n and a + ve rational number a  

Surd Quant Notes | EduRev 

ii) If n is a positive integer and a, b are rational numbers then

Surd Quant Notes | EduRev  

 iii) If n is a + ve integer and a, b are rational numbers then

Surd Quant Notes | EduRev 

iv) If m and n are positive integers and a is a positive rational number then

Surd Quant Notes | EduRev

 v) If m and n are positive integers and a is a positive rational number then

Surd Quant Notes | EduRev

 

ORDER AND BASE OF SURDS

Surd Surd Quant Notes | EduRev is a surd of nth order with base a. Surd Quant Notes | EduRev is a quadratic surd

 Surd Quant Notes | EduRev  is a cubic surd

 Surd Quant Notes | EduRev is a biquadratic surd

 Pure surds and mixed surds. A surd which does not have a rational factor other than unity (1) is called a pure surd. For example Surd Quant Notes | EduRev etc. are pure surds.

A surd which has a rational factor other than unity, the other factor being rational is called a mixed surd e.g. Surd Quant Notes | EduRevSurd Quant Notes | EduRev etc are mixed surds.

 Conversion of mixed surds into pure surds. 

 Example: Express each of the following as pure surds

Surd Quant Notes | EduRev 

Solution:

Surd Quant Notes | EduRev 

Surd Quant Notes | EduRev 

Surd Quant Notes | EduRev

 Surd Quant Notes | EduRev

 Surd Quant Notes | EduRev

                

To express the given surds as mixed surds in its simplest form 

 Example 1: Express each of the following as mixed surds in its simplest form

Surd Quant Notes | EduRev

 Solution

Surd Quant Notes | EduRev
Surd Quant Notes | EduRev
Surd Quant Notes | EduRev

 conversion of a surd into a surd of given order

 step I Obtain the order of given surd say n

step II Obtain the order of new surd into which the given surd is to be converted say m

step III compute m/n let m/n = k

step IV write the new surd as Surd Quant Notes | EduRev

 

Example 1

Convert  Surd Quant Notes | EduRev into a surd of order 6

Solution: n = order of given surd = 2

m= order of new surd = 6

Let K = m/n = 6/2 = 3

So Surd Quant Notes | EduRev

Example 2

Convert Surd Quant Notes | EduRev into a surd of order 8

Solution

Here n = 2

M = 8

K = m/n = 8/2 = 4.

So Surd Quant Notes | EduRev

Example 3: Convert Surd Quant Notes | EduRev into a surd of order 6

Solution:

Here n = 3

M = 6

K = m/n = 6/3 = 2

So Surd Quant Notes | EduRev

 

Example 4: Express 2 x Surd Quant Notes | EduRev  as pure Surd of order 6

Solution:

Surd Quant Notes | EduRev

 

Now n = 3

       m = 6

 k = Surd Quant Notes | EduRev

So given surd = Surd Quant Notes | EduRev     

 Example 5: Express Surd Quant Notes | EduRev as pure surd of order 4

Solution: 

Surd Quant Notes | EduRev

Surd Quant Notes | EduRev

Here n = 2

        M = 4

Surd Quant Notes | EduRev 

Conversion of two or more surds into surds of the same order.

Step 1.Let the surds be Surd Quant Notes | EduRev

So that then order are n1, n2, n3 …….. etc

Step II Find out LCM of n1, n2, n3 ………. xn

                                    = n (say)

Step III Compute Surd Quant Notes | EduRev  and

    Step IV Write the requested surd as

Surd Quant Notes | EduRev 

Example 1: Convert Surd Quant Notes | EduRev into surds of the same but smallest order

Solution: n1 = order of Surd Quant Notes | EduRev =4

            n= order of Surd Quant Notes | EduRev = 6

 n = LCM of 4 and 6 – 12

Now m1 = Surd Quant Notes | EduRev 

So Surd Quant Notes | EduRev

 and  Surd Quant Notes | EduRev

So required surds are Surd Quant Notes | EduRev

 Example 2: Convert Surd Quant Notes | EduRev andSurd Quant Notes | EduRev into surds of same but smallest order

n1 = order of the surd Surd Quant Notes | EduRev

n2 = order of the surd Surd Quant Notes | EduRev

   n = LCM of 2, 3, = 6.

Now m1
Surd Quant Notes | EduRev Hence 

    Thus reqd. surds are Surd Quant Notes | EduRev

 Comparison of surds.

If the surds are of the same order, they can be compared by comparing their radicands.

 Example 3: Which surd is larger Surd Quant Notes | EduRev or Surd Quant Notes | EduRev

Solution: Given surds are of the same order and their radicands are 26 and 35 respectively

   Since 35 > 26 so Surd Quant Notes | EduRev

 

Example 4: Arrange the following surds in ascending order Surd Quant Notes | EduRev

Solution: Surds are of the same order

   So Surd Quant Notes | EduRev

 

Comparing the surds of distinct order

We first reduce them to the same but smallest order and then compare their radiants.

 Example 5 : Which surd is larger Surd Quant Notes | EduRev

Solution: Order of the two surds is 3, 4

   Their LCM is 12

Surd Quant Notes | EduRev

Example 6: Which is greater Surd Quant Notes | EduRev

n1 = 2   n2 = 3

n = LCM of 2, 3 = 6

Surd Quant Notes | EduRev
Surd Quant Notes | EduRev

 

Example 7: Arrange the following surds in ascending order of magnitude Surd Quant Notes | EduRev

Solution: Given surd are Surd Quant Notes | EduRev

   The order of these surds is 2, 3, 6

  LCM of 2, 3, 6 is 6

 The surds can be written as

   Surd Quant Notes | EduRev

Surd Quant Notes | EduRev

Surd Quant Notes | EduRev

Surd Quant Notes | EduRevas it is

Now compare the radiants

Surd Quant Notes | EduRev

 ADDITION AND SUBTRACTION OF SURDS

 Surds having same irrational factor are called similar surds. e.g. Surd Quant Notes | EduRev are similar surds. such type of surds can be added or subtracted. Where as unlike surds having no common irrational factor cannot be added or subtracted.  

Surd Quant Notes | EduRev

 If the surds are unlike, reduce each of them to its simplest form and express each in such a way that they have a common irrational factor.

 

Example 1: Simplify Surd Quant Notes | EduRev

Solution: Surd Quant Notes | EduRev

Surd Quant Notes | EduRev 

Example 2: Simplify Surd Quant Notes | EduRev

Solution:

Surd Quant Notes | EduRev

Surd Quant Notes | EduRev

Surd Quant Notes | EduRev

Surd Quant Notes | EduRev

Example 3: Simplify 2 Surd Quant Notes | EduRev

Solution: 

Surd Quant Notes | EduRev
Surd Quant Notes | EduRev

 

 Multiplication of Surds

Surds of the same order can e multiplied

Surd Quant Notes | EduRev

If the surds are not of the same order, they can be multiplied after converting them to surds of the same order

Surd Quant Notes | EduRev

Division of Surds

a. Surds of the same order may  be divided

            Surd Quant Notes | EduRev

e.g 4

Surd Quant Notes | EduRev

Surd Quant Notes | EduRev

RATIONALISING FACTOR

 i) If the product of two surds is a rational number then each one of them is called the rationalizing factor of the other.

Surd Quant Notes | EduRev

Surd Quant Notes | EduRev

CONJUGATE SURD

Surd Quant Notes | EduRev are conjugate surds

Dynamic Test

Content Category

Related Searches

Semester Notes

,

MCQs

,

study material

,

Surd Quant Notes | EduRev

,

past year papers

,

Summary

,

Surd Quant Notes | EduRev

,

pdf

,

practice quizzes

,

Sample Paper

,

mock tests for examination

,

Important questions

,

Surd Quant Notes | EduRev

,

Exam

,

Extra Questions

,

shortcuts and tricks

,

Viva Questions

,

Objective type Questions

,

video lectures

,

ppt

,

Previous Year Questions with Solutions

,

Free

;