Can be written as a rational number ?

Question

KnowledgeBoat · Accepted Answer

No, cannot be written as a rational number . Proof by contradiction : Assume is rational. Then it can be expressed as , where p and q are integers with q ≠ 0 and gcd(p, q) = 1 (lowest form). Squaring both sides : This means p2 is even, and so p must also be even. Let p = 2k for some integer k. Then : This means q2 is even, so q is also even. But, both p and q being even contradicts our assumption that gcd(p, q) = 1. Hence, our assumption is wrong. Hence, cannot be written as . It is an irrational number.

Mathematics

Can be written as a rational number ?

Whole Numbers

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