Question

Which least number must be subtracted to 1025 to make a perfect square? (Use Long division method).

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (A)

$1$

The following steps to find the square root by long division method
1. Draw lines over pairs of digits from right to left.
2. Find the greatest number whose square is less than or equal to the digits in the first group.
3. Take this number as the divisor and quotient of the first group and find the remainder.
4. Move the digits from the second group besides the remainder to get the new dividend.
5. Double the first divisor and bring it down as the new divisor.
6. Complete the divisor and continue the division.
7. Repeat the process till the remainder becomes zero

Divisor $\downarrow$	Quotient $\downarrow$ 32
3	$\overline{10}$ $\overline{25}$ 9
62	125 124
	1$\leftarrow$ Remainder

The remainder is 1. it represents that the square of 32 is less than 1025 by 1.
Therefore, a perfect square will be obtained by subtracting 1 from the given number 1025.
So, perfect square = 1025 - 1 = 1024