Related things - Square roots

Ö2
The diagram shows a right angle triangle where sides a and b are equal. By Pythagoras's theorem, a²+b²=c². Therefore for this triangle, c²=2a². When a = 1, c²=2 therefore c =

Ö2 and Ö3
This diagram again shows a right angle triangle ABC with two equal sides. When a = 1, c = Ö2. Also shown is a circle centre C with radius CD and the line CE which is perpendicular to AC.
Using Pythagoras's theorem in the triangle ACE, AE²=AC²+CE². Therefore, when a = 1, AC = Ö2 and AE²=2+1, so AE = Ö3.