Question

prove that √3 is an irrational number​

Answer 1

Let us assume the contrary that root 3 is rational

then √3 = p/q, where p, q are the integers i.e., p, q Z and co-primes, i.e., GCD (p,q) = 1. Here 3 is the prime number that divides p2, then 3 divides p and thus 3 is a factor of p.

Answer 2

Answer:

Root 3 is irrational is proved by the method of contradiction. If root 3 is a rational number, then it should be represented as a ratio of two integers. We can prove that we cannot represent root is as p/q and therefore it is an irrational number.

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