Question Number 39799 by tapukumar056@gmail.com last updated on 11/Jul/18
$$\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{will}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{makes}}\:\mathrm{680621} \\ $$$$\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{perfect}}\:\boldsymbol{\mathrm{square}}\:\boldsymbol{\mathrm{root}}? \\ $$
Answered by $@ty@m last updated on 11/Jul/18
$$\mathrm{8}\mid\mathrm{680621}\mid\mathrm{825} \\ $$$$\mathrm{8}\mid\mathrm{64} \\ $$$$........... \\ $$$$\mathrm{162}\mid\mathrm{406} \\ $$$$\:\:\:\:\:\mathrm{2}\mid\:\mathrm{324} \\ $$$$................ \\ $$$$\mathrm{1645}\mid\:\:\mathrm{8221} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{5}\mid\:\:\mathrm{8225}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$................... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(−\mathrm{4}\right) \\ $$$$\therefore\:\mathrm{4}\:{should}\:{be}\:{added}\:{to}\:\mathrm{680621}\: \\ $$$${in}\:{order}\:{to}\:{make}\:{it}\:{a}\:{perfect}\: \\ $$$${square}. \\ $$