To find the squares of numbers between 25 and 75,
- 462,50−46=4 and 42=16. Then, 46−25=21
∴462=2116 - Similarly, for 632,63−50=13 and 132=169. Then, 63−25=38.
So, last two digits will be 69 and before that add the residual 1 from 169 to 38 which is 38 + 1 = 39.
∴632=3969 To find the squares of numbers between 75 and 125,
- For 942, 100 - 94 = 6 and 62=36.
As
94<100, subtract 6 from 94 i.e., 94 - 6 = 88.
∴942=8836 - Similarly, for 1072, 107 - 100 = 7 and 72=49.
So, 49 will be first two digits of the square from right. As
107>100, add 7 to 107 i.e., 107 + 7 = 114.
∴1072=11449 Alternatively, 46 < 63 < 94 < 107.
So,
462<632<942<1072 ∴ Match the given squares in this order.