Question

write the lowest number of six digit . b what smallest number should it be divided so that it becomes a perfect square?

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}, \\ \mathrm{smallest}\mathrm{six}\mathrm{digit}\mathrm{number}=100000 \\ \mathrm{Now},\mathrm{prime}\mathrm{factorisation}\mathrm{of}100000\mathrm{is}, \\ 100000=\underline{2\times 2}\times \underline{2\times 2}\times 2\times \underline{5\times 5}\times \underline{5\times 5}\times 5 \\ \mathrm{Since}\mathrm{the}\mathrm{prime}\mathrm{factor}2\mathrm{and}5\mathrm{do}\mathrm{not}\mathrm{occur}\mathrm{in}\mathrm{pair}\mathrm{so}\mathrm{it}\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{perfect}\mathrm{square}. \\ \mathrm{In}\mathrm{order}\mathrm{to}\mathrm{make}\mathrm{it}\mathrm{a}\mathrm{perfect}\mathrm{square},\mathrm{it}\mathrm{must}\mathrm{be}\mathrm{divided}\mathrm{by}10\left(2\times 5\right). \\ \mathrm{Now},\frac{100000}{10}=10000,\mathrm{that}\mathrm{is}\mathrm{a}\mathrm{perfect}\mathrm{square}. \\ \mathrm{Also},\sqrt{10000}=100 \end{gathered}$$