Prove that √7 is an irrational number.

Question

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 7 divides 7q², so 7 divides p² but 7 is prime Let p = 7m, where m is an integer. Substituting this value of p in (i), we get As 7 divides 7m², so 7 divides q² but 7 is prime Thus, p and q have a common factor 7. 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 √7 is an irrational number.

Rational Irrational Nos

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