Question

Prove that √3 is an irrational number.​

Answer 1

here is your answer mate:

let us assume that √3 is a rational number

then there exists two integers 'a' and 'b' such that

√3 = a/b (where both 'a' and 'b' are co-prime)

squaring on both sides

3 = a^2/b^2

3b^2 = a^2 ___ i

3 divides a^2

thus, three divides 'a' ___ii

a = 3c (for some inteder 'c')

squaring at both sides

a^2 = 9c^2

3b^2 = 9c^2 ___ from i

b^2 = 3c^2

three divides b^2

thus, three divides 'b'___ iii

from ii and iii

3 is a common factor of 'a' and 'b'

but this is not possible as 'a' and 'b' are coprime

thus, our assumption is wrong

thus, √3 is irrational

hence proved!!

hope this answer helps you buddy

please mark as brainliest:-)

Answer 2

Answer:

It is a irrational number