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Answer :
(i)
\(\qquad \begin{array}{c|lcr}
&20\\
\hline
2 &\;\; \;\bar{4}\bar{02}\\
&-4\\
\hline
4 &\;\;\; 02\\
\hline
\end{array}
\)
So we have got remainder as 2.So we can say that 2 is the smallest required number to be subtracted from 402 to get a perfect square./br>
Therefore, we have new number as :402-2=400
So, \(\sqrt{400}=20\)
(ii)
\(\qquad \begin{array}{c|lcr}
&44\\
\hline
4 &\;\; \;\bar{19}\bar{89}\\
&-16\\
\hline
84 &\;\;\; 389\\
&\;\;\; 336\\
\hline
&\;\;\;53\\
\hline
\end{array}
\)
So we have got remainder as 53.So we can say that 53 is the smallest required number to be subtracted from 1989 to get a perfect square./br>
Therefore, we have new number as :1989-53=1936
So, \(\sqrt{1936}=44\)
(iii)
\(\qquad \begin{array}{c|lcr}
&57\\
\hline
5 &\;\; \;\bar{32}\bar{50}\\
&-25\\
\hline
107 &\;\;\; 750\\
&\;\;\; 749\\
\hline
&\;\;\;1\\
\hline
\end{array}
\)
So we have got remainder as 1.So we can say that 1 is the smallest required number to be subtracted from 3250 to get a perfect square./br>
Therefore, we have new number as :3250-1=3249
So, \(\sqrt{3249}=57\)
(iv)
\(\qquad \begin{array}{c|lcr}
&28\\
\hline
2 &\;\; \;\bar{8}\bar{25}\\
&-4\\
\hline
48 &\;\;\; 425\\
&\;\;\; 384\\
\hline
&\;\;\;41\\
\hline
\end{array}
\)
So we have got remainder as 41.So we can say that 41 is the smallest required number to be subtracted from 825 to get a perfect square./br>
Therefore, we have new number as :825-41=784
So, \(\sqrt{784}=28\)
(v)
\(\qquad \begin{array}{c|lcr}
&63\\
\hline
6 &\;\; \;\bar{40}\bar{00}\\
&-36\\
\hline
123 &\;\;\; 400\\
&\;\;\; 369\\
\hline
&\;\;\;31\\
\hline
\end{array}
\)
So we have got remainder as 31.So we can say that 31 is the smallest required number to be subtracted from 4000 to get a perfect square./br>
Therefore, we have new number as :4000-31=3969
So, \(\sqrt{3969}=63\)