How to Calculate the Square Root of Any Number, Digit by Digit Method

Video Description

MIT and Harvard entrance exams specifically tested if students knew how to calculate square roots by hand. In this video I will teach you the square root algorithm to calculate the square root of any number, digit by digit, by hand without a calculator. 0:00 Intro 3:47 2025 7:48 831744 10:50 13689 13:18 11.56 15:15 1234 19:12 531.5 23:47 inventor 25:15 why it works 28:58 place value Harvard 1869 problem https://graphics8.nytimes.com/packages/pdf/education/harvardexam.pdf MIT exam 1876 https://web.archive.org/web/20190404065722/https://libraries.mit.edu/archives/exhibits/exam-entrance1876/arithmetic1876.html Naval Mathematics, 1966 https://www.google.com/books/edition/Mathematics/Bcs6iIbOp9EC?hl=en&gbpv=1 Goals for the Correlation of Elementary Science and Mathematics, 1969 https://archive.org/details/goalsforcorrelat0000unkn/page/50/mode/2up Aryabhata's methods https://arxiv.org/pdf/math/0608793 Translation of Sanskrit https://www.ganitamkalakriyagolam.com/post/vargam%C5%ABla Route to Learn https://www.youtube.com/watch?v=nuZr4hAYfzU Āryabhaṭa's Algorithmic Square Rooting https://itihaasa.substack.com/p/aryabhats-algorithmic-square-rooting The square root algorithm https://www.cantorsparadise.com/the-square-root-algorithm-f97ab5c29d6d Byjus https://byjus.com/maths/square-root/ Find Square Root by Hand without Calculator https://www.youtube.com/watch?v=AMnDmDOXH04 Square root algorithm https://www.basic-mathematics.com/square-root-algorithm.html Calculating Square Root by Hand (Early Grades) https://www.youtube.com/watch?v=x4D5bPqONAE Ancient formula calculate ANY square root https://youtu.be/MXveVqBxFow Abacus picture https://en.wikipedia.org/wiki/Abacus#/media/File:Houghton_Typ_520.03.736_-_Margarita_philosophica.jpg Margarita philosophica nova https://archive.org/details/margaritaphiloso00reis_2/page/n191/mode/2up 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 Members get early access to videos YouTube members https://www.youtube.com/channel/UCHnj59g7jezwTy5GeL8EA_g/join Patreon members https://www.patreon.com/mindyourdecisions Support the channel with a one-time donation https://www.paypal.com/donate/?hosted_button_id=REZRY3QRQPYQA Subscribe: https://www.youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay. Book ratings are from January 2025. My Books (worldwide links) https://mindyourdecisions.com/blog/my-books/#worldwide My Books (US links) Mind Your Decisions: Five Book Compilation https://amzn.to/2pbJ4wR A collection of 5 books: "The Joy of Game Theory" rated 4.2/5 stars on 564 reviews http://amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.2/5 stars on 55 reviews http://amzn.to/1o3FaAg "40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 81 reviews http://amzn.to/1LOCI4U "The Best Mental Math Tricks" rated 4.3/5 stars on 148 reviews http://amzn.to/18maAdo "Multiply Numbers By Drawing Lines" rated 4.5/5 stars on 57 reviews http://amzn.to/XRm7M4 Mind Your Puzzles: Collection Of Volumes 1 To 3 https://amzn.to/2mMdrJr A collection of 3 books: "Math Puzzles Volume 1" rated 4.4/5 stars on 138 reviews http://amzn.to/1GhUUSH "Math Puzzles Volume 2" rated 4.2/5 stars on 45 reviews http://amzn.to/1NKbyCs "Math Puzzles Volume 3" rated 4.3/5 stars on 38 reviews http://amzn.to/1NKbGlp 2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter. My Blog https://mindyourdecisions.com/blog/ Twitter https://twitter.com/preshtalwalkar Instagram https://www.instagram.com/preshtalwalkar/ Merch https://teespring.com/stores/mind-your-decisions Patreon https://www.patreon.com/mindyourdecisions Press https://mindyourdecisions.com/blog/press