how to prove that root 5 is irrational
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it can not be written in form of p/q (q is not 9)
harjwantsingh12:
Let us assume root 5 is a rational number
So we can write it root5/1 = p/q, where p and q are co prime integers and q is not equal to zero
S. B. S (root 5)^2 = p^2/q^2 5=p^2/q^2
No we interchange the digit
p,q also are intigers
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Chandan answered 11 month(s) ago
Prove that root 5 is irrational.
Prove that root 5 is irrational
Class-X Maths
person
Asked by Meghasri
Sep 7
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person
Syeda , SubjectMatterExpert
Member since Jan 25 2017
Answer.
let root 5 be rational
then it must in the form of p/q [q is not equal to 0][p and q are co-prime]
root 5=p/q
=> root 5 * q = p
squaring on both sides
=> 5*q*q = p*p ------> 1
p*p is divisible by 5
p is divisible by 5
p = 5c [c is a positive integer] [squaring on both sides ]
p*p = 25c*c --------- > 2
sub p*p in 1
5*q*q = 25*c*c
q*q = 5*c*c
=> q is divisble by 5
thus q and p have a common factor 5
there is a contradiction
as our assumsion p &q are co prime but it has a common factor
so √5 is an irrational
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Chandan answered 11 month(s) ago
Prove that root 5 is irrational.
Prove that root 5 is irrational
Class-X Maths
person
Asked by Meghasri
Sep 7
3 Likes
39430 views
editAnswer
Like Follow
4 Answers
Top Recommend
| Recent
person
Syeda , SubjectMatterExpert
Member since Jan 25 2017
Answer.
let root 5 be rational
then it must in the form of p/q [q is not equal to 0][p and q are co-prime]
root 5=p/q
=> root 5 * q = p
squaring on both sides
=> 5*q*q = p*p ------> 1
p*p is divisible by 5
p is divisible by 5
p = 5c [c is a positive integer] [squaring on both sides ]
p*p = 25c*c --------- > 2
sub p*p in 1
5*q*q = 25*c*c
q*q = 5*c*c
=> q is divisble by 5
thus q and p have a common factor 5
there is a contradiction
as our assumsion p &q are co prime but it has a common factor
so √5 is an irrational
I hope you like it if you like this answer please mark me as a brain list
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