You are Here: Home » Math Concepts » Some squares and cubes you should know

Some squares and cubes you should know

What is a square?

When a number is multiplied by itself, the result is called the square of that number.
For example, 3 * 3 = 9.  This is the same as saying 3 squared, or written with an exponent as 32, and 9 is called the square of 3. This type of calculation is used frequently in math.  Many formulas and calculations require multiplying a number by itself.  It can be useful to have the squares of some basic numbers in memory to help with estimations and to help understand the way the squares get bigger quickly.

Here are some basic squares – take a few minutes to learn some of these by heart.  You will use them more often than you think.

02 = 0

12 = 1

22 = 4

32 = 9

42 = 16

52 = 25

62 = 36

72 = 49

82 = 64

92 = 81

102 = 100

112 = 121

122 = 144

132 = 169

142 = 196

152 = 225

162 = 256

202 = 400

252 = 625

302 = 900

402 = 1600

502 = 2500

What is a cube?

A cube is similar to a square, but you multiply the number by itself a third time to get the cube.
For example: 3 * 3 * 3 = 27, so 27 is the cube of 3.  The exponent looks like 33. It is also useful to know a few of these, take a minute and learn some of the cubes below.

03 = 0

13 = 1

23 = 8

33 = 27

43 = 64

53 = 125

103 = 1000

123 = 1728

163 = 4096

203 = 8000

253 = 15625

403 = 64000

503 = 125000

1003 = 1000000