Perfect Square List 1 to 1000: Understanding the Numbers that Square Up

The first step is to observe that

1. The final number in every perfect square is either 1, 4, 5, 6, 9 or 00. 

Now, do the following tests after removing the zeros from all integers that finish in 1, 4, 5, 6, and 9, as well as any numbers that end in even zeros: 

2. Digital roots are available in 1, 4, 7, and 9. Unless its digital root is one of the following: 1, 4, 7, or 9, a number cannot be a perfect square. (To determine a number’s digital root, sum all of its digits. Add the digits of this amount if it is greater than 9. The number’s digital root is the single digit that can be found at the end.) 

3. If the unit digit is 5, the tenth digit will always be 2. 

4. Unless the number ends in 6, the tenth digit is always even (1, 3, 5, 7, and 9). That means the tenth digit is always even if it ends in 1, 4, or 9. (2, 4, 6, 8, 0). 

5. When a number is divided by 8 and its square is divisible by 4, it has a 0 as the final result. 

6. When an even number is squared and not divisible by 4, it always leaves a remnant of 4, yet when an odd number is squared and divisible by 8, it always leaves a remainder of 1. 

7. A perfect square’s total number of prime factors is always odd.