Question

Question 5 (ii)
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:

1750

Answer 1

1750

$\begin{array}{cc}& 41\\ 4& \overline{17}\overline{50}\\ & -16\\ 81& 150\\ & -81\\ & 69\end{array}$

Since remainder is 69. Therefore ${41}^2<1750$

Next perfect square number ${42}^2=1764$

Hence, number to be added = 1764 – 1750 =14

$\therefore 1750+14=1764$

Hence, the square root of 529 is 42.