Question

Match the given numbers to the smallest number that has to be subtracted from it to get a perfect square.

• A. 22
• B. 0.0
• C. 76

Answer 1

By applying long division method to find the square root of 1786.

$$\begin{array}{cc}& 42\\ 4& \overline{17}\overline{86}\\ & 16\\ 82& 186\\ & 164\\ & 22\end{array}$$

$\text{Remainder = 22.}$

$\text{Hence,}(1786-22)\text{is a perfect square.}$
So, 22 must be subtracted from 1786 to make it a perfect square.

Similarly, for 3325,
$$\begin{array}{cc}& 57\\ 5& \overline{33}\overline{25}\\ & 25\\ 107& 825\\ & 749\\ & 76\end{array}$$
Remainder = 76
$\therefore$ 76 must be subtracted from 3325 to make it a perfect a square.

But when we apply long division method for 2401,
$\begin{array}{cc}& 49\\ 4& 2401\\ & 16\\ 89& 801\\ & 801\\ 98& 0\end{array}$

The remainder is 0. So, 2401 is a perfect square.
$\therefore$ There is no need to subtract anything from 2401.