Find the smallest positive integer n such that sqrtx-sqrt(x-1)<0.01

Answer 1

sqrt x = sqrt(x-1) + 0.01
x = (x-1) + 0.02 sqrt(x-1) + 0.0001
0.02 sqrt (x-1) = 0.9999
sqrt (x-1) = 49.995
x-1 = 2499.5
x = 2500.5