Prove that √6 is an irrational number.

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KnowledgeBoat · Accepted Answer

Suppose that is a rational number, then where p, q are integers, q ≠ 0 and p, q have no common factors (except 1) As 2 divides 6q², so 2 divides p² but 2 is prime Let p = 2k, where k is some integer. Substituting this value of p in (i), we get As 2 divides 2k², so 2 divides 3q² 2 divides 3 or 2 divides q² But 2 does not divide 3, therefore, 2 divides q² 2 divides q (Theorem 1) Thus, p and q have a common factor 2. This contradicts that p and q have no common factors (except 1). Hence, our supposition is wrong. Therefore, is not a rational number. So, we conclude that is an irrational number.

Mathematics

Prove that √6 is an irrational number.

Rational Irrational Nos

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