I saw somewhere a screenshot from a old(?) Russian cartoon with the following math inside. On a screenshot one can see that a student successfully solves 2 exercises on finding square root and receives an excellent mark.
Here are the important bits:
Left exercise Compute $\sqrt{9 511 936}$ with $0.01$ precision \begin{align} \newcommand\ph[1]{\color{white}{#1}} &\ph{60}\hspace{-1em}\sqrt{9'51'19'56'} = 3084.14\\ &\ph{60}9\\ &\overline{608|511'9}\\ &\ph{60}8|1364\\ &\overline{6164|2555'6}\\ &\ph{608}4|24656\\ &\overline{61631|\ph{0}9000'0}\\ &\ph{6080}1|\ph{0}61681\\ &\overline{616834|283190'0}\\ &\ph{60803}4|2467296\\ &\overline{\ph{616834|2}364604}\\ \end{align} Answer $3084.14$
Right exercise Find $\sqrt{123904}$ \begin{align} \newcommand\ph[1]{\color{white}{#1}} &\hspace{-1em}\sqrt{12'39'04} = 352\\ &\ph{1}9\\ &\overline{65|33'9}\\ &\ph{6}5|325\\ &\overline{702|140'4}\\ &\ph{60}2|1404\\ &\overline{\ph{702|2}0}\\ \end{align}
Answer is $352$
My thoughts. I understand the part of splitting the number by two digits. I understand the first step of guessing the first digit, but then I have no idea what is going on. Who they get $65$ in the second example? Could one guess the whole procedure or give a link explaining it? Thanks!