Question

Prove that root 3 is an irrational number. (250 words)​

Answer 1

Step-by-step explanation:

let us consider that root 3 is an irrational number

two integers a and b such that

root 3 =a÷b

where a and b are coprime.

now

root 3 =a÷b

=(b root3)^2 =a^2 [ squaring both sides ]

= a^2= 3 b^2 ---------------(i)

a square is divisible by 3

a is also divisible by 3

a=3c

(i) = a^2= 3b^2

= (3c)^2 = 3b^2

=9c^2 =3b^2

= b^2 =3c^2

b square is divisible by 3

b is also divisible by 3

but it contradict the fact that a and b are coprime so our considerations is wrong

root is a irrational number.