Question

prove that
$\sqrt{3}$
is irrational

Answer 1

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Answer 2

Let us assume that √3 is rational

Let √3=a/b { where a and b be any integer and b≠0 , a and b are the co-primes}

=>(√3)²=a²/b²

=>3=a²/b²

=>a²=3b².........1

Where a² is divisible by 3
And a is also divisible by 3

Again, let =3c. {for some integer c}

a²=(3c)² {squaring both side}

=>3b²=6c² {form 1}

=>b²=3c²

Therefore b² is divisible by 3
Also b is divisible by 3

Therefore a and b have atleast 3 as a common factor

This contradicts the fact that a and b are co primes

So our assumption is wrong

Therefore √3 is irrational .