Question

least positive whole number that must be subtracted from9545 ,so that the resultant number is a perfect square

Answer 1

To find the perfect square number first we find the square root of 9545 as;
$$\begin{gathered} 97 \\ 9\left|\overline{95}\overline{45}\right| \\ +9\left|81\right| \\ \overline{187\left|1445\right|} \\ 1309 \\ \overline{136} \end{gathered}$$
Since the remainder is 136.
Therefore the least number to be subtracted from 9545 is 136 to get a perfect square.
And the perfect square number will be (9545 - 136) = 9409
and the square root of 9409 is;
$$\begin{gathered} 97 \\ 9\left|\overline{94}\overline{09}\right| \\ +9\left|81\right| \\ \overline{187\left|1309\right|} \\ 1309 \\ \overline{0} \end{gathered}$$
Therefore the square root of 9409 is 97.