Question

Find the least number which must be subtracted from 18265 to make it a perfect square. [4 MARKS]

Answer 1

Concept : 1 Mark
Division method : 2 Marks
Conclusion : 1 Mark

Applying the long division method, we have

$\begin{array}{cc}& 135\\ 1& 1\overline{82}\overline{65}\\ & 1\\ 23& 082\\ & 069\\ 265& 1365\\ & 1325\\ & 40\end{array}$

We find that the remainder is 40 instead of 0.

It means that if 40 is subtracted from 18265, then the remainder will be '0' and the new number will be a perfect square.

Hence, the required least number is 40.