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EXAMPLE $2$ Find the square roots of (i) $11$.$7649$ and (ii) $0$.$076176$ .$\newline$Solution$\newline$(i) \begin{tabular}{r|c}$\newline$$3$ & $\overline{11 .} \overline{76} \overline{49}$ \\$\newline$+$3$ & $-9$ \\$\newline$\hline $64$ & $276$ \\$\newline$+$4$ & $-256$ \\$\newline$\hline $683$ & $2049$ \\$\newline$$3$ & $-2049$ \\$\newline$\hline & $x$$\newline$\end{tabular}$\newline$$$\therefore \sqrt{11.7649}=3.43 \text {. }$$$\newline$Note The decimal point is placed in the quotient when the first pair decimal part (i.e. $76$ ) is written in the dividend.$\newline$(ii) \begin{tabular}{r|r} $2$ &.$\overline{07} \overline{61} \overline{76} \quad(.276$ \\ +$2$ & $-4$ \end{tabular}$\newline$$$\therefore \sqrt{0.076176}=0.276$$