Question 24
Let $A_0 = (0, 0).$ Distinct points $A_1,$ $A_2,$ $\ldots$ lie on the $x$-axis, and distinct points $B_1,$ $B_2,$ $\ldots$ lie on the graph of $y = \sqrt{x}.$ For every positive integer $n,$ $A_{n-1}B_nA_n$ is an equilateral triangle. What is the least $n$ for which the length $A_0A_n \ge 100?$