MIT Entrace Exam Arithmetic 1876 WayBackMachine:
https://web.archive.org/web/20190404065722/https://libraries.mit.edu/archives/exhibits/exam-entrance1876/arithmetic1876.html
Square root method Burning Math
http://burningmath.blogspot.com/2013/09/extracting-square-roots-mentally-at.html
Square root method proof Math StackExchange
https://math.stackexchange.com/questions/2069192/why-does-this-method-for-finding-the-square-root-of-a-number-work
Square root method Grey Matters
http://gmmentalgym.blogspot.com/2010/10/root-extractions.html#rtsqr
Hindu-Arabic numeral system
https://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_system
Laplace quote
https://en.wikipedia.org/wiki/History_of_the_Hindu%E2%80%93Arabic_numeral_system#Impact_on_arithmetic
Laplace picture
https://en.wikipedia.org/wiki/File:Laplace,_Pierre-Simon,_marquis_de.jpg
Abacus picture
https://en.wikipedia.org/wiki/Abacus#/media/File:Houghton_Typ_520.03.736_-_Margarita_philosophica.jpg
A similar method to extract the cube root of number in your head explained in this video:
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