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Perfect Squares & Perfect Cubes
A number is a perfect square when it can be made by multiplying a whole number by itself. A number is a perfect cubewhen the same whole number is used as a factor three times.
Perfect square6² = 6 × 6 = 36
Perfect cube4³ = 4 × 4 × 4 = 64
Numbers 1–50
Perfect Squares
Square means “raise to the second power.”
1²1
2²4
3²9
4²16
5²25
6²36
7²49
8²64
9²81
10²100
11²121
12²144
13²169
14²196
15²225
16²256
17²289
18²324
19²361
20²400
21²441
22²484
23²529
24²576
25²625
26²676
27²729
28²784
29²841
30²900
31²961
32²1,024
33²1,089
34²1,156
35²1,225
36²1,296
37²1,369
38²1,444
39²1,521
40²1,600
41²1,681
42²1,764
43²1,849
44²1,936
45²2,025
46²2,116
47²2,209
48²2,304
49²2,401
50²2,500
Perfect-square radicands
Perfect Square Roots
The square root reverses the squaring operation.
√11
√42
√93
√164
√255
√366
√497
√648
√819
√10010
√12111
√14412
√16913
√19614
√22515
√25616
√28917
√32418
√36119
√40020
√44121
√48422
√52923
√57624
√62525
√67626
√72927
√78428
√84129
√90030
√96131
√1,02432
√1,08933
√1,15634
√1,22535
√1,29636
√1,36937
√1,44438
√1,52139
√1,60040
√1,68141
√1,76442
√1,84943
√1,93644
√2,02545
√2,11646
√2,20947
√2,30448
√2,40149
√2,50050
Numbers 1–50
Perfect Cubes
Cube means “raise to the third power.”
1³1
2³8
3³27
4³64
5³125
6³216
7³343
8³512
9³729
10³1,000
11³1,331
12³1,728
13³2,197
14³2,744
15³3,375
16³4,096
17³4,913
18³5,832
19³6,859
20³8,000
21³9,261
22³10,648
23³12,167
24³13,824
25³15,625
26³17,576
27³19,683
28³21,952
29³24,389
30³27,000
31³29,791
32³32,768
33³35,937
34³39,304
35³42,875
36³46,656
37³50,653
38³54,872
39³59,319
40³64,000
41³68,921
42³74,088
43³79,507
44³85,184
45³91,125
46³97,336
47³103,823
48³110,592
49³117,649
50³125,000
Perfect-cube radicands
Perfect Cube Roots
The cube root reverses the cubing operation.
∛11
∛82
∛273
∛644
∛1255
∛2166
∛3437
∛5128
∛7299
∛1,00010
∛1,33111
∛1,72812
∛2,19713
∛2,74414
∛3,37515
∛4,09616
∛4,91317
∛5,83218
∛6,85919
∛8,00020
∛9,26121
∛10,64822
∛12,16723
∛13,82424
∛15,62525
∛17,57626
∛19,68327
∛21,95228
∛24,38929
∛27,00030
∛29,79131
∛32,76832
∛35,93733
∛39,30434
∛42,87535
∛46,65636
∛50,65337
∛54,87238
∛59,31939
∛64,00040
∛68,92141
∛74,08842
∛79,50743
∛85,18444
∛91,12545
∛97,33646
∛103,82347
∛110,59248
∛117,64949
∛125,00050
Work backward
Squares, Cubes, and Roots Are Connected
A root asks which number was multiplied by itself. Because 9² = 81, √81 = 9. Because 5³ = 125, ∛125 = 5.
9² = 81⇄√81 = 95³ = 125⇄∛125 = 5
★Quick Memory Tip
Look for patterns instead of memorizing everything at once. The last digit of perfect squares follows repeating patterns, and the difference between consecutive squares increases by consecutive odd numbers.