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Answer :
(i)
\(\qquad \begin{array}{c|lcr}
&48\\
\hline
4 &\;\; \;\bar{23}\bar{04}\\
&-16\\
\hline
88 &\;\;\;\;\; 704\\
&\;\;\;\;\; 704\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{2304}=48\)
(ii)
\(\qquad \begin{array}{c|lcr}
&67\\
\hline
6 &\;\; \;\bar{44}\bar{89}\\
&-36\\
\hline
127 &\;\;\;\;\; 889\\
&\;\;\;\;\; 889\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{4489}=67\)
(iii)
\(\qquad \begin{array}{c|lcr}
&59\\
\hline
5 &\;\; \;\bar{34}\bar{81}\\
&-25\\
\hline
109 &\;\;\;\;\; 981\\
&\;\;\;\;\; 981\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{3481}=59\)
(iv)
\(\qquad \begin{array}{c|lcr}
&23\\
\hline
2 &\;\; \;{5}\bar{29}\\
&-4\\
\hline
43 &\;\;\;\;\; 129\\
&\;\;\;\;\; 129\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{529}=23\)
(v)
\(\qquad \begin{array}{c|lcr}
&57\\
\hline
5 &\;\; \;\bar{32}\bar{49}\\
&-25\\
\hline
107 &\;\;\;\;\; 749\\
&\;\;\;\;\; 749\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{3249}=57\)
(vi)
\(\qquad \begin{array}{c|lcr}
&37\\
\hline
3 &\;\; \;\bar{13}\bar{69}\\
&\;-9\\
\hline
67 &\;\;\;\;\;469\\
&\;\;\;\;\; 469\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{1369}=37\)
(vii)
\(\qquad \begin{array}{c|lcr}
&76\\
\hline
7 &\;\; \;\bar{57}\bar{76}\\
&-49\\
\hline
146 &\;\;\;\;\; 876\\
&\;\;\;\;\; 876\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{5776}=76\)
(viii)
\(\qquad \begin{array}{c|lcr}
&89\\
\hline
8 &\;\; \;\bar{79}\bar{21}\\
&-64\\
\hline
169 &\;\;\;\;\; 1521\\
&\;\;\;\;\; 1521\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{7921}=89\)
(ix)
\(\qquad \begin{array}{c|lcr}
&24\\
\hline
2 &\;\; \;5\bar{76}\\
&-4\\
\hline
44 &\;\;\;\;\; 176\\
&\;\;\;\;\; 176\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{576}=24\)
(x)
\(\qquad \begin{array}{c|lcr}
&32\\
\hline
3 &\;\; \;\bar{10}\bar{24}\\
&-9\\
\hline
62 &\;\;\;\;\; 124\\
&\;\;\;\;\; 124\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{1024}=32\)
(xi)
\(\qquad \begin{array}{c|lcr}
&56\\
\hline
5 &\;\; \;\bar{31}\bar{36}\\
&-25\\
\hline
106 &\;\;\;\;\; 636\\
&\;\;\;\;\; 636\\
\hline
&\;\;\;\;\; 0\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{3136}=56\)
(xii)
\(\qquad \begin{array}{c|lcr}
&30\\
\hline
3 &\;\; \;9\bar{00}\\
&-9\\
\hline
&\;\;\;\;\; 00\\
\hline
\end{array}
\)
Hence we have, \(\sqrt{900}=30\)