Question

Find the least number which must be added to 306452 to make it a perfect square.

• A. 345
• B. 465
• C. 464
• D. 324

Answer 1

The correct option is C

464

We use long division method to find the square root of 306452. For that, we will group 2 numbers from right to left and then proceed with the division.

$\begin{array}{cc}& 553\\ 5& \overline{30}\overline{64}\overline{52}\\ & -25\\ 105& 564\\ & -525\\ 1103& 3952\\ & -3309\\ & 643\end{array}$

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