Square root

${\begin{array}{rrr|rrr}&&&2&5&6\\\hline &&{\sqrt {}}&6&55&36\\{\underline {2}}\times {\underline {2}}&=&4&-4&\downarrow &\downarrow \\\hline 2\times 2&=&4~~&2&55&\downarrow \\4{\underline {5}}\times {\underline {5}}&=&225&-2&25&\downarrow \\\hline 25\times 2&=&50~~&&30&36\\50{\underline {6}}\times {\underline {6}}&=&3036&&-30&36\\\hline &&&&&0\end{array}}$

${\sqrt {65536}}=256$

The method is based on the identity

$(10x+y)^{2}=100x^{2}+20xy+y^{2}$.