INTRODUCTION
In mathematics,an irrational factor is a number that cannot put in the form of P/Q (i.e fraction of two integers), where P and Q are integers and Q is not equal to zero.Now such numbers that are not rational are termed as irrational.Irrational number (or factor) is a set of real numbers.
Example:- ,where x= 2,3,5 etc.
Any irrational factor may be represented as a non-terminating decimal or as a non-recurring decimal(a number in which not allow repeated number up to infinity) and conversely .This means, it has infinite expansion which cannot be put as a fraction
.e.g:- .3333333........................ is a recurring infinite expansion as 3 repeats itself infinitely.Now .333........... can be put as a fraction ; hence it is a rational number.
Any root of an arithmetical numbers whose value cannot be accurately determined is called a surd.All surds are irrational numbers,but all irrational numbers are not surds.
Example:- The base of logarithm e is irrational but not surd.The value of e =2.71828..... which is non-terminating and non-recurring decimal.
I am planning to write more post on simplify algebraic fractions, solve this math problem for me. Keep checking my blog.
Irrational Factors-rationalising Factors
Some times when we multiply two irrational number then there product becomes rational number.In this case each of the irrational number is called a RATIONALISING FACTOR to the other.
Example:(i)(√3 ) x (√3 ) = [(√3)2] = 3,which is rational number.So,we can say that ,√3 is a rationalising factor of a √3 .
(ii) (√3 + √2) x (√3 - √2) = [(√3)2 - (√2)2] = 3 - 2 = 1 which is a rational number.So we can say that , (√3 + √2) and (√3 - √2) are rationalising factors of each other.
Properties of Irrational Factors
There are mainly three types of properties in irrational factors.
1. ORDER Properties:- For any irrational factors a,b any one of the following relationals is true
a>b,a<b
Again for a>b>c,we have a>c
or for a<b<c,we get a<c
2. ADDITIVE Properties:-For any irrational factors a,b,c all these relationals is true
(i) Commutative :- a+b=b+a
(ii) Associative :- a+(b+c)=(a+b)+c
(iii) Identity(zero) :- a+0=0+a=a
(iv )Inverse :- a+ (-a)=0,Here (-a) is additive inverse of a.
(v) Cancellation :- If a+c=b+c then a=b
3. MULTICATIVE Properties:- For any irrational factors a,b,c all these relationals is true
(i) Commutative : a.b= b.a
(ii) Associative :- a.(b.c)=(a.b).c
(iii) Identity :- a X1=1X a=a
(iv) Inverse :- a.1/a = 1
(v) Cancellation :- If a.c = b.c then a=b
In mathematics,an irrational factor is a number that cannot put in the form of P/Q (i.e fraction of two integers), where P and Q are integers and Q is not equal to zero.Now such numbers that are not rational are termed as irrational.Irrational number (or factor) is a set of real numbers.
Example:- ,where x= 2,3,5 etc.
Any irrational factor may be represented as a non-terminating decimal or as a non-recurring decimal(a number in which not allow repeated number up to infinity) and conversely .This means, it has infinite expansion which cannot be put as a fraction
.e.g:- .3333333........................ is a recurring infinite expansion as 3 repeats itself infinitely.Now .333........... can be put as a fraction ; hence it is a rational number.
Any root of an arithmetical numbers whose value cannot be accurately determined is called a surd.All surds are irrational numbers,but all irrational numbers are not surds.
Example:- The base of logarithm e is irrational but not surd.The value of e =2.71828..... which is non-terminating and non-recurring decimal.
I am planning to write more post on simplify algebraic fractions, solve this math problem for me. Keep checking my blog.
Irrational Factors-rationalising Factors
Some times when we multiply two irrational number then there product becomes rational number.In this case each of the irrational number is called a RATIONALISING FACTOR to the other.
Example:(i)(√3 ) x (√3 ) = [(√3)2] = 3,which is rational number.So,we can say that ,√3 is a rationalising factor of a √3 .
(ii) (√3 + √2) x (√3 - √2) = [(√3)2 - (√2)2] = 3 - 2 = 1 which is a rational number.So we can say that , (√3 + √2) and (√3 - √2) are rationalising factors of each other.
Properties of Irrational Factors
There are mainly three types of properties in irrational factors.
1. ORDER Properties:- For any irrational factors a,b any one of the following relationals is true
a>b,a<b
Again for a>b>c,we have a>c
or for a<b<c,we get a<c
2. ADDITIVE Properties:-For any irrational factors a,b,c all these relationals is true
(i) Commutative :- a+b=b+a
(ii) Associative :- a+(b+c)=(a+b)+c
(iii) Identity(zero) :- a+0=0+a=a
(iv )Inverse :- a+ (-a)=0,Here (-a) is additive inverse of a.
(v) Cancellation :- If a+c=b+c then a=b
3. MULTICATIVE Properties:- For any irrational factors a,b,c all these relationals is true
(i) Commutative : a.b= b.a
(ii) Associative :- a.(b.c)=(a.b).c
(iii) Identity :- a X1=1X a=a
(iv) Inverse :- a.1/a = 1
(v) Cancellation :- If a.c = b.c then a=b
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