a Cambridge interview problem: sqrt(3-2sqrt(2))=

Behind the number: both the sqrt(3-2sqrt(2)) and sqrt(2)-1 are the results of tan(22.5 degrees) when you use different versions of the half-angle identity. This video shows you how to make them equal without using a calculator. check out the special right triangle: sqrt(3-2sqrt(2))=? nested square roots, Simplify nested square roots, Completing the square for square root. Math for fun, tan(22.5), tan(22.5) with half angle formula, blackpenredpen