Prove that 1/√11 is an irrational number.

Question

Prove that 1/√11  is an irrational number.

KnowledgeBoat · Accepted Answer

Let be a rational number, then where p, q are integers, q ≠ 0 and p, q have no common factors (except 1) As 11 divides 11p², so 11 divides q² but 11 is prime Let q = 11m, where m is an integer. Substituting this value of q in (i), we get As 11 divides 11m², so 11 divides p² but 11 is prime Thus, p and q have a common factor 11. This contradicts that p and q have no common factors (except 1). Hence, is not a rational number. So, we conclude that is an irrational number.

Mathematics

Prove that 1/√11 is an irrational number.

Rational Irrational Nos

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