(adsbygoogle = window.adsbygoogle || []).push({}); Proof by Induction--Sqrt(n)

1. The problem statement, all variables and given/known data

Prove that if a line of unit length is given, then a line of length sqrt(n) can be constructed for each n.

2. Relevant equations

N/A

3. The attempt at a solution

So I'm not really sure where to begin...I assumed that a unit length is the representation of the natural numbers (1, 2, 3...n). And then I drew a triangle with unit length 1 on the legs and then constructed the hypotenuse to be sqrt(2). And then I drew a triangle with unit length 1 on a leg and unit length 2 on a leg and then I constructed the hypotenuse to be sqrt(5). But I don't know how to:

i) Write this as a formal proof by induction, or

ii) How to find some sqrt(n) with unit lengths, like sqrt(3) or sqrt(4).

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# Proof by Induction-Sqrt(n)

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