Prove that√3. is irrational
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Hey mate here's your answer
let us asaum that √3 is an irrational number
a and b are coprime number
√3=a/b
√3b=a
on squaring in both the sides
(√3b) ^2=a^2
3b^2=a^2...............(I)
a^2 is divisible by 3
a will also be divisible by 3
a=3m where m is an integer
Put the value of a in equation (I)
3b^2=(3m) ^2
3b^2=9m^2
b^2=3m^2
b^2 is divisible by 3
b is also divisible by 3
But we assumed that a and b are co-prime
our assumption was wrong
√3 is an irrational
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