Simple Rules for Perfect Squares

Lets look at the first 10 perfect squares and we will observe some properties.

1² =1

2² =4

3² =9

4² =16

5² =25

6² =36

7² =49

8² =64

9² =81

10² =100

0 through 9 represent the units digits of all numbers.  

Our numbers show: 

All numbers that end in 1 or 9 will produce a units digit of 1.

All numbers that end in a 2 or a 8 will produce a units digit of 4.

All numbers that ends in a 3 or a 7 will produce a units digit of 9.

All numbers that end in 5 will produce a units digit of 5.

All numbers that end in 0 will produce a units digit of 0.

We know that any number that ends in 2, 3, 7, or 8 does not have a perfect square.

32, 87,63, 1028 are not perfect squares.

In all perfect squares, they have twice the number of zeros as the number being squared.  All perfect squares have an even number of zeros.

20, 3,000, 40,000 are not perfect squares.

60²=3600 (2 zeros)
1100²=1,210,000 (4 zeros)

49000²=2,401,000,000 (6 zeros)

Exercises:

Which of the following could be perfect squares based on the rules we presented.

121, 310, 278, 6400, 497, 1,000, 2,500, 529

Perfect square is the square of an integer. 3² =9 so 9 is a perfect square.  20 is the result of (√20)² and √20 does not produce a integer therefore 20 is not a perfect square.