Question

Prove that Under root 3 is an irrational number.
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Answer 1

Answer:

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Answer 2

Answer:

Let us assume that root 3 is rational, so we can find two integers such that root 3 = p/q where p and q are co- primes.

p = q root 3

p² = 3q² ==> p²/3 = q²

If 3 divides p², 3 divides p also

ie, 3 is a factor of p

p= 3a ==> p² = 9 a²

3q² = 9a² ==> q² = 3a² ==> a² = q²/3

If 3 divides q² , 3 divides q also

ie, 3 is a factor of q

Ie, p and q have no common factors

Hence , our assumption is wrong.

THEREFORE root 3 is irrational.

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