Question

Self Practice 3C Find the square root of each of the following numbers by long division method. 1. (a) 484 (f) 6724 (b) 841 (c) 1849 (d) 2704 (g) 7569 (h) 9801​

Answer 1

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

$\rm :\longmapsto\:1. \: \: \sqrt{484}$

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:22 \:\:}}}\\ {\underline{\sf{2}}}& {\sf{\:\:484 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \:4 \:  \:  \:  \:  \:\:}} \\ {\underline{\sf{42}}}& {\sf{\:\: \: \: 084   \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: 84 \:  \:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: \: \: \:0 \:\:}} \end{array}\end{gathered}\end{gathered}$

$\bf\implies \: \sqrt{484} = 22$

$\rm :\longmapsto\:2. \: \: \sqrt{6724}$

$\red{\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:82 \:\:}}}\\ {\underline{\sf{8}}}& {\sf{\:\:6724 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \:64 \:  \:  \:  \:  \:\:}} \\ {\underline{\sf{162}}}& {\sf{\:\: \: \: \: 324   \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 324 \:  \:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: \: \: \:0 \:\:}} \end{array}\end{gathered}\end{gathered}}$

$\bf\implies \: \sqrt{6724} = 82$

$\rm :\longmapsto\:3. \: \: \sqrt{841}$

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:29 \:\:}}}\\ {\underline{\sf{2}}}& {\sf{\:\:841 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \:4 \:  \:  \:  \:  \:\:}} \\ {\underline{\sf{49}}}& {\sf{\:\: \: \: 441   \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 441 \: \:  \:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: \: \: \:0 \: \: \:\:}} \end{array}\end{gathered}\end{gathered}$

$\bf\implies \: \sqrt{841} = 29$

$\rm :\longmapsto\:4. \: \: \sqrt{1849}$

$\red{\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:43 \:\:}}}\\ {\underline{\sf{4}}}& {\sf{\:\:1849 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \:16 \:  \:  \:  \:  \:\:}} \\ {\underline{\sf{83}}}& {\sf{\:\: \: \: \: 449\:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: 449 \:  \:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: \: \: \:0 \:\:}} \end{array}\end{gathered}\end{gathered}}$

$\bf\implies \: \sqrt{1849} = 43$

$\rm :\longmapsto\:5. \: \: \sqrt{2704}$

$\blue{\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:52 \:\:}}}\\ {\underline{\sf{5}}}& {\sf{\:\:2704 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \:25 \:  \:  \:  \:  \:\:}} \\ {\underline{\sf{102}}}& {\sf{\:\: \: \: \: 204\:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: 204 \:  \:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: \: \: \:0 \:\:}} \end{array}\end{gathered}\end{gathered}}$

$\bf\implies \: \sqrt{2704} = 52$

$\rm :\longmapsto\:6. \: \: \sqrt{7569}$

$\green{\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:87 \:\:}}}\\ {\underline{\sf{8}}}& {\sf{\:\:7569 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \:64 \:  \:  \:  \:  \:\:}} \\ {\underline{\sf{167}}}& {\sf{\:\: \: \: 1169\:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \:1169 \:  \:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: \: \: \:0 \:\:}} \end{array}\end{gathered}\end{gathered}}$

$\bf\implies \: \sqrt{7569} = 87$

$\rm :\longmapsto\:7. \: \: \sqrt{9801}$

$\green{\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:99 \:\:}}}\\ {\underline{\sf{9}}}& {\sf{\:\:9801 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \:81 \:  \:  \:  \:  \:\:}} \\ {\underline{\sf{189}}}& {\sf{\:\: \: \: 1701\:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \:1701 \:  \:}} \\ {\underline{\sf{}}}& {\sf{\: \: \: \: \: \:0 \:\:}} \end{array}\end{gathered}\end{gathered}}$

$\bf\implies \: \sqrt{9801} = 99$