What least number must be added to 4812 to make the sum a perfect square? (Use Long division method).
A
86
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B
88
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C
89
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D
85
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Solution
The correct option is B88 The following steps are used 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 ↓
Quotient ↓ 69
6
¯¯¯¯¯¯48¯¯¯¯¯¯12 36––––
129
1212 1161–––––
51
Here, the remainder =51 We observe here 692<4812<702 The required number to be added =702−4812 =4900−4812 =88 Therefore, 88 must be added to 4812 to make it a perfect square.