Prove: If n &#x2208;<!-- ∈ --> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double

Aidyn Cox

Aidyn Cox

Answered question

2022-05-24

Prove: If n N is not the square of some other m N , then n must be irrational.

Answer & Explanation

extractumzz

extractumzz

Beginner2022-05-25Added 9 answers

Let n be a positive integer such that there is no m such that n = m 2 . Suppose n is rational. Then there exists p and q with no common factor ( b e s i d e 1) such that
n = p q
Then
n = p 2 q 2
However, n is an positive integer and p and q have no common factors beside 1. So q = 1. This gives that
n = p 2
Contradiction since it was assumed that n m 2 for any m.

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