Given: a unit length.
Use only a straightedge (ruler without markings) & a compass.
Prove: we can construct a line segment of √n for all n ∈N.
Proof:
1) n=1 (given).
2) Assume true for n, i.e. can construct √n
3) Construct a right-angled triangle with height = 1, base= √n
=> hypotenuse = $latex sqrt {n+1} $
=> True for n+1
Therefore true for all n ∈N [QED]
Mathtuition88 