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1.Find the square root of each of the following numbers by Long Division method.
(i) 2304

(ii) 4489

(iii) 3481

(iv) 529

(v) 3249

(vi) 1369

(vii) 5776

(viii) 7921

(ix) 576

(x) 1024

(xi) 3136

(xii) 900

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, \(\sqrt{900}=30\)