Question

Find the square root of these numbers by division method (all steps)(photos)
a) 121
b) 225
c) 441
d) 1225
e) 4096
f) 24964​

Answer 1

$\large\underline{\sf{Solution-a}}$

$\rm \: \sqrt{121}$

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{11}}}\\ {\underline{\sf{1}}}& {\sf{121}} \\{\sf{}}& \underline{\sf{1 \: \: \: \: }} \\ {\underline{\sf{21}}}& {\sf{021}} \\{\sf{}}& \underline{\sf{ \: \: 21}} \\ {\underline{\sf{}}}& {\sf{ \: \: 0}} \end{array}\end{gathered}\end{gathered}$

$\rm\implies \: \sqrt{121} = 11$

$\large\underline{\sf{Solution-b}}$

$\rm \: \sqrt{225}$

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{15}}}\\ {\underline{\sf{1}}}& {\sf{225}} \\{\sf{}}& \underline{\sf{1 \: \: \: \: }} \\ {\underline{\sf{25}}}& {\sf{125}} \\{\sf{}}& \underline{\sf{ 225}} \\ {\underline{\sf{}}}& {\sf{ \: \: 0}} \end{array}\end{gathered}\end{gathered}$

$\rm\implies \: \sqrt{225} = 15$

$\large\underline{\sf{Solution-c}}$

$\rm \: \sqrt{441}$

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{21}}}\\ {\underline{\sf{2}}}& {\sf{441}} \\{\sf{}}& \underline{\sf{4 \: \: \: \: }} \\ {\underline{\sf{41}}}& {\sf{041}} \\{\sf{}}& \underline{\sf{ \: \: 41}} \\ {\underline{\sf{}}}& {\sf{ \: \: 0}} \end{array}\end{gathered}\end{gathered}$

$\rm\implies \: \sqrt{441} = 21$

$\large\underline{\sf{Solution-d}}$

$\rm \: \sqrt{1225}$

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{35}}}\\ {\underline{\sf{3}}}& {\sf{1225}} \\{\sf{}}& \underline{\sf{9 \: \: \: \: }} \\ {\underline{\sf{65}}}& {\sf{325}} \\{\sf{}}& \underline{\sf{ 325}} \\ {\underline{\sf{}}}& {\sf{ \: \: 0}} \end{array}\end{gathered}\end{gathered}$

$\rm\implies \: \sqrt{1225} = 35$

$\large\underline{\sf{Solution-e}}$

$\rm \: \sqrt{4096}$

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{64}}}\\ {\underline{\sf{6}}}& {\sf{4096}} \\{\sf{}}& \underline{\sf{36 \: \: \: \: }} \\ {\underline{\sf{124}}}& {\sf{496}} \\{\sf{}}& \underline{\sf{ 496}} \\ {\underline{\sf{}}}& {\sf{ \: \: 0}} \end{array}\end{gathered}\end{gathered}$

$\rm\implies \: \sqrt{4096} = 64$

$\large\underline{\sf{Solution-f}}$

$\rm \: \sqrt{24964}$

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{158}}}\\ {\underline{\sf{1}}}& {\sf{24964}} \\{\sf{}}& \underline{\sf{1 \: \: \: \: \: \: \: \: }} \\ {\underline{\sf{25}}}& {\sf{149 \: \: \: \: }} \\{\sf{}}& \underline{\sf{125 \: \: \: \: }}\\ {\underline{\sf{308}}}& {\sf{ \: \: 2494}} \\{\sf{}}& \underline{\sf{ \: \: 2494}} \\ {\underline{\sf{}}}& {\sf{ \: \: 0}} \end{array}\end{gathered}\end{gathered}$

$\rm\implies \: \sqrt{24964} = 158$

Hence,

$\begin{gathered}\boxed{\begin{array}{c|c} \bf & \bf \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf \sqrt{121} & \sf 11\\ \\ \sf \sqrt{225} & \sf 15 \\ \\ \sf \sqrt{441} & \sf 21\\ \\ \sf \sqrt{1225} & \sf 35\\ \\ \sf \sqrt{4096} & \sf 64 \\ \\ \sf \sqrt{24964} & \sf 158\end{array}} \\ \end{gathered}$