Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Prove that  is an irrational number.      

Prove that \sqrt{3} is an irrational number.

 

 
 
 
 
 

Answers (1)

Let us assume that \sqrt{3} be rational no.

So, \sqrt{3} = \frac{p}{q} where p and q are co-primes and q \neq 0

    \\ \Righararrow p = \sqrt{3}q\\\Rightarrow p^2 = 3q^2\quad-(i)

\therefore 3 divides p2 i.e,    3 also divides p    -(ii)

Let p = 3m for some integer m.

From eq(i)    9m^2 = 3q^2

    \Rightarrow q^2 = 3m^2

So, 3 divides q2 i.e,    3 divides q also -(iii)

From (ii) and (iii), we get that 3 divided p and q both which is a contradiction to the fact that p and q are co-primes.

Hence our assumption is wrong.

So, \sqrt{3} is an irrational number.

Posted by

Safeer PP

View full answer

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 10, 12 syllabus 2024-25 out; board restores two-level mathematics rule
anam-khan

CBSE Class 10 board exam 2024 passing criteria, eligibility for compartment; all you need to know

Latest Question