Question

The greatest 5 digit perfect square number is .

• A. 99856
• B. 99525
• C. 99256
• D. 99552

Answer 1

The correct option is A 99856

Greatest 5 digit number = 99999.

We need to find out the smallest number that must be subtracted from 99999 to get a perfect square.

Applying the division method:
$$\begin{array}{cc}& 316\\ 3& \overline{9}\overline{99}\overline{99}\\ & 9\downarrow \\ 61& 99\\ & 61\\ 626& 3899\\ & 3756\\ & 143\end{array}$$

We can observe that 143 is the remainder.

So, if we subtract 143 from 99999, we will get a perfect square,

Largest 5 digit perfect square = 99999 - 143

= 99856.