User blog comment:DrCocktor/Almost 102^2 pages/@comment-34876209-20191116161134

To mentally square numbers near 100 with ease, use the algebraic property that \((a + b)\cdot (a - b) + b^2= a^2\). Therefore \(117^2\) would be \((117 + 17)\cdot (117 - 17) + 17^2 = 134\cdot 100 + 289 = 13400 + 289 = 13689\). By memorizing the first 50 squares you can therefore square any three digit number. (I.e. \(864^2 = (864 + 36)\cdot (864 - 36) + 36^2 = 900\cdot 828 + 1296 = 745200 + 1296 = 746496\).