Proof: <msqrt> 13 </msqrt>

Oakey1w

Oakey1w

Answered question

2022-06-16

Proof: 13 is irrational

Answer & Explanation

Haggar72

Haggar72

Beginner2022-06-17Added 25 answers

Consider the polynomial x 2 13 Z [ x ] . The rational root theorem guarantees its roots aren't rational and since 13 is a root of the polynomial, it is irrational.
Zion Wheeler

Zion Wheeler

Beginner2022-06-18Added 11 answers

A number is irrational, if you can not find a finite continued fraction.
Now try to write 13 as continued fraction and you'll see, its periodic:
13 = [ 3 ; 1 , 1 , 1 , 1 , 6 ¯ ]

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