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3.Find the square root of the following decimal numbers.
(i) 2.56

(ii) 7.29

(iii) 51.84

(iv) 42.25

(v) 31.36


Answer :

(i)
\(\qquad \begin{array}{c|lcr} &1.6\\ \hline 1 &\;\; \;\bar{2.}\bar{56}\\ &-1\\ \hline 26 &\;\;\; 156\\ &\;\;\; 156\\ \hline &\;\;\;\;\; 0\\ \hline \end{array} \)

Hence we have, \(\sqrt{2.56}=1.6\)

(ii)
\(\qquad \begin{array}{c|lcr} &2.7\\ \hline 2 &\;\; \;\bar{7.}\bar{29}\\ &-4\\ \hline 47 &\;\;\; 329\\ &\;\;\; 329\\ \hline &\;\;\;\;\; 0\\ \hline \end{array} \)

Hence we have, \(\sqrt{7.29}=2.7\)

(iii)
\(\qquad \begin{array}{c|lcr} &7.2\\ \hline 7 &\;\; \;\bar{51.}\bar{84}\\ &-49\\ \hline 142 &\;\;\; 284\\ &\;\;\; 284\\ \hline &\;\;\;\;\; 0\\ \hline \end{array} \)

Hence we have, \(\sqrt{51.84}=7.2\)

(iv)
\(\qquad \begin{array}{c|lcr} &6.5\\ \hline 6 &\;\; \;\bar{42.}\bar{25}\\ &-36\\ \hline 125 &\;\;\; 625\\ &\;\;\; 625\\ \hline &\;\;\;\;\; 0\\ \hline \end{array} \)

Hence we have, \(\sqrt{42.25}=6.5\)

(v)
\(\qquad \begin{array}{c|lcr} &5.6\\ \hline 5 &\;\; \;\bar{31.}\bar{36}\\ &-25\\ \hline 106 &\;\;\;\;\; 636\\ &\;\;\;\;\; 636\\ \hline &\;\;\;\;\; 0\\ \hline \end{array} \)

Hence we have, \(\sqrt{31.36}=5.6\)