Prove that √5 is irrational number.

Question

KnowledgeBoat · Accepted Answer

Let be rational. Thus, can be expressed in the form of . As 5 divides 5q2, so 5 divides p2 but 5 is prime, Thus, 5 divides p. Let p = 5m for some positive integer m. Then, p = 5m Substituting this value of p in (1), we get : As 5 divides 5m2, so 5 divides q2 but 5 is prime. Thus, 5 divides q. This shows that 5 is a common factor of p and q. This contradicts the hypothesis that p and q have no common factor, other than 1. is not a rational number. Hence, proved that is a irrational number.

Mathematics

Prove that √5 is irrational number.

Rational Irrational Nos

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