MathDB
MMO 224 Moscow MO 1952 square of number begins with 0.9...9

Source:

August 8, 2019
number theoryPerfect Square

Problem Statement

a) Prove that if the square of a number begins with 0.9...9⏟1000.\underbrace{\hbox{9...9}}_{\hbox{100}}, then the number itself begins with 0.9...9⏟1000.\underbrace{\hbox{9...9}}_{\hbox{100}},.
b) Calculate 0.9...9\sqrt{0.9...9} (6060 nines) to 6060 decimal places
Back to ProblemsView on AoPS