Think Carefully Part 3

Number Theory Level 1

If $\sqrt 2$ is expressed as a fraction in the lowest form, $\frac ab$ for coprime positive integers $a,b$ , what is the last digit of $a-b$ ?

See Part 1 , and Part 2 .

7 0 6 This question is flawed 8 9

2 solutions

Venkata Karthik Bandaru
May 7, 2015

$\sqrt{2}$ is an irrational number, and thus by definition there do not exist positive coprime integers $a$ and $b$ such that $\sqrt{2} = \dfrac{a}{b}$ .

See this if you guys are interested in various proofs of irrationality of $\sqrt{2}$ , my favourite one being the proof by contradiction, and upvote if you like. For any clarifications, comment below,

Désire Désire
Dec 27, 2018

$\sqrt{2}$ doesn't have it's own exact fraction form $\frac {a}{b}$ and it will never be , since $\sqrt{2}$ is an irrational number.

Think Carefully Part 3

2 solutions

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