A List of Perfect Squares
Perfect squares are numbers that are created when you take a whole number times itself. They are used in many different topics in algebra, including factoring and radicals, and also in other disciplines like geometry.
1^{2} 
= 
1 
26^{2} 
= 
676 

2^{2} 
= 
4 
27^{2} 
= 
729 
3^{2} 
= 
9 
28^{2} 
= 
784 
4^{2} 
= 
16 
29^{2} 
= 
841 
5^{2} 
= 
25 
30^{2} 
= 
900 
6^{2} 
= 
36 
31^{2} 
= 
961 
7^{2} 
= 
49 
32^{2} 
= 
1024 
8^{2} 
= 
64 
33^{2} 
= 
1089 
9^{2} 
= 
81 
34^{2} 
= 
1156 
10^{2} 
= 
100 
35^{2} 
= 
1225 
11^{2} 
= 
121 
36^{2} 
= 
1296 
12^{2} 
= 
144 
37^{2} 
= 
1369 
13^{2} 
= 
169 
38^{2} 
= 
1444 
14^{2} 
= 
196 
39^{2} 
= 
1521 
15^{2} 
= 
225 
40^{2} 
= 
1600 
16^{2} 
= 
256 
41^{2} 
= 
1681 
17^{2} 
= 
289 
42^{2} 
= 
1764 
18^{2} 
= 
324 
43^{2} 
= 
1849 
19^{2} 
= 
361 
44^{2} 
= 
1936 
20^{2} 
= 
400 
45^{2} 
= 
2025 
21^{2} 
= 
441 
46^{2} 
= 
2116 
22^{2} 
= 
484 
47^{2} 
= 
2209 
23^{2} 
= 
529 
48^{2} 
= 
2304 
24^{2} 
= 
576 
49^{2} 
= 
2401 
25^{2} 
= 
625 
50^{2} 
= 
2500 
Why Are They Called "Perfect Squares?" 
Multiplying a number by itself is given this special name because of the geometrical interpretation. Think of the dimensions of a rectangle. If the numbers are not the same, then you will have an imperfect rectangle. But if the dimensions are the same, meaning the length is the same size as the width, then your rectangle will become a square that is perfect.
Take a look at the figure below to get an idea what we are talking about.
Notice how when the dimensions are the same it creates a square, but when they are different it creates a rectangle. This is why they are called perfect squares! 


What do you think a perfect cube is? Think about the dimensions of a cube vs. the dimensions of a prism (a box).
I bet you figured it out: A perfect cube is something like 3^{3}. A short list of perfect cubes are 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
View more pre algebra math problems or visit the GradeA homepage.
