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The smallest natural number that must be added to 650 to make it a perfect square is:
25
26
15
11
26
Given: The number to be modified is 650.
The number to be modified is 650.
252=625,262=676
Locate 650 between two consecutive squares. Since 252=625 and 262=676, the smallest number to add to reach the next perfect square is 676тИТ650.
Many students subtract 650 from the smaller square (625), resulting in a negative value, or they mistake the 'nearest' square (676) for the 'previous' square (625).
Estimate the square root
Calculate the squares of numbers near the square root of 650. Since 625тАЛ=25 and 676тАЛ=26, the number 650 lies between these two perfect squares.
252<650<262
Identify the next perfect square
To make 650 a perfect square by addition, we must reach the next integer square, which is 262=676.
262=676
Calculate the difference
Subtract the given number from the next perfect square to find the value to be added.
676тИТ650=26
B is correct because the next perfect square after 650 is 676, and 676тИТ650=26.
This logic is essential for questions involving 'smallest number to be subtracted' or 'smallest number to be added', which frequently appear in LCM/HCF and Algebra problems involving surds.