Question

Question 4 (ii)
Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained:

1989

Answer 1

1989

$\begin{array}{cc}& 44\\ 4& \overline{19}\overline{89}\\ & -16\\ 84& 389\\ & -336\\ & 53\end{array}$

We know that, of we subtract the remainder from the number, we get a perfect square.

Here, we get remainder 53. Therefore 53 must be subtracted from

1989 to get a perfect square.

$\therefore 1989-53=1936$

$\begin{array}{cc}& 44\\ 4& \overline{19}\overline{36}\\ & -16\\ 84& 336\\ & -336\\ & 0\end{array}$

Hence, the square root of 1936 is 44.