how to prove √3 irrational

Asked by asmitjain2006 | 18th Mar, 2020, 09:47: PM

Expert Answer:

how to prove √3 irrational.
Let us assume that rational number.
Hence, it can be expressed as in the form of p/q.
√3 = p/q
p = √3 q
p2 = 3q
p2 is divisble by 3 then p is also divisble by 3
So p = 3k for some integer k
p2 = 9k2
3q2 = 3(3k2
q2 = 3k2
q2/3 = k2
Hence, 3 divides q2 
3 divides q also
3 divides p and q hence 3 is a factor of both p and q
therefore p and q are not co-prime.
Hence our assumption is wrong. 
So, √3 is irrational.

Answered by Sneha shidid | 19th Mar, 2020, 11:09: AM