Question

Question 5 (v)
Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

6412

Answer 1

6412

$\begin{array}{cc}& 80\\ 8& \overline{64}\overline{12}\\ & -64\\ 160& 0012\\ & -0000\\ & 12\end{array}$

Since remainder is 12. Therefore ${80}^2<6412$

Next perfect square number ${81}^2=6561$

Hence, number to be added = 6561 – 6412 = 149

$\therefore 6412+149=6561$

Hence, the square root of 6561 is 81.