Question

What least number must be added to 700 to make the sum a perfect square? (Use Long division method).

• A. 25
• B. 26
• C. 28
• D. 29

Answer 1

Answer: (D)

29

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 $\downarrow$ 26
2	$\overline{7}$ $\overline{00}$ 4
46	300 276
	24$\leftarrow$ Remainder

We observe here ${26}^2<700<{27}^2$
The required number to be added = ${27}^2-700$
= 729 - 700
= 29
Therefore, 29 must be added to 700 to make it a perfect square.