Question

Prove that
$\sqrt{3}$
is an irrational number.​

Answer 1

Answer:

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Answer 2

Answer:

let us assume that root 3 is a rational no.

therefore,

root 3 = a/b , where a and b are co primes.

on squaring both side we get ,

3 b² = a²

=> 3 divides a² so , 3 divides a also

let a = 3m for some integers m

from above we get

3 m² = b²

=> 3 divides b² , so 3 divides b also

so, 3 is a common factor of a and b

this contradicts our assumptions that p and q are co primes.

therefore, root 3 is irrational no.

hence proved.