Question

Find the least number which must be added to 306452 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,

$\begin{array}{cc}& 553\\ 5& 306452\\ & 25\\ 105& 564\\ & 525\\ 1103& 3952\\ & 3309\\ & 643\end{array}$

From above, it is clear that given number 306452 is greater than $(553{)}^2$

$i.e.,{553}^2<306452<306916(i.e.,{554}^2)$

Therefore, if we add 306916 - 306452 = 464 to 306452 then the sum 306452 + 464 will be a perfect square.

So, the required least number is 464.