Question

Prove that root 3 is an irrational number.​

Answer 1

To be contrary √3 is a rational number such that √3=a/b

√3b=a

√3b^2=a^2. (squaring both side

3b^2=a^2

b^2=a^2/3

since a^2 is divisible by 3 and a is also divisible by 3

a/3=c

a=3c

√3b=3c

√3b)^2=3c^2 (squaring both side

3b^2=9c^2

b^2=9c^2/3.

b^2=3c^2

c^2=b^2/3

since b^2 is divisible by 3 and b is also divisible by 3

since it contradict our fact that a and b are co prime so √3 is a irrational number

please follow me