Question

prove that root 3, is irrational

Answer 1

,hope mine answer helps you

Answer 2

Hey mate !!
Here is your solution

Let us suppose that root 3 is a rational number.
√3 = p/q , where p and q are co prime and q not equal to 0.

Squaring both the sides, we get ,
3 = p²/ q²
3q² = p² ........................( i )
=> p ² is divisible by 3.

So, p is also divisible by 3.

Let p = 3m for some integer m.

Substituting p = 3m in (i ) we, get,
3q² = (3m)² = 9m²
q² = 3m².
=> q² is divisible by 3.
So, q is also divisible by 3.

Since p and q both are divisible by 3, therefore 3 is a common factor of both p and q . But this contradicts our assumption that p and q are co prime .

This is bcoz of our contradictory assumption that √3 us a rational number.

Hence √3 is an irrational number.


Hope this will help you

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