Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

B: Powers and Roots

Table B1

\(n\) \(n^{2}\) \(\sqrt{n}\) \(n^{3}\) \(\sqrt[3]{n}\)
1 1 1 1 1
2 4 1.414214 8 1.259921
3 9 1.732051 27 1.442250
4 16 2 64 1.587401
5 25 2.236068 125 1.709976
6 36 2.449490 216 1.817121
7 49 2.645751 343 1.912931
8 64 2.828427 512 2
9 81 3 729 2.080084
10 100 3.162278 1,000 2.154435
11 121 3316625 1,331 1.223980
12 144 3.464102 1,728 2.289428
13 169 3.605551 2,197 2.351335
14 196 3.741657 2,744 2.410142
15 225 3.872983 3,375 2,466212
16 256 4 4,096 2.519842
17 289 4.123106 4,913 2.571282
18 324 4.242641 5,832 2.620741
19 361 4.358899 6,859 2.668402
20 400 4.472136 8,000 2.714418
21 441 4.582576 9,261 2.758924
22 484 4.690416 10,648 2.802039
23 529 4.795832 12,167 2.843867
24 576 4.898979 13,824 2.884499
25 625 5 15,625 2.924018
26 676 5.099020 17,576 2.962496
27 729 5.196152 19,683 3
28 784 5.291503 21,952 3.036589
29 841 5.385165 24,389 3.072317
30 900 5.477226 27,000 3.107233
31 961 5.567764 29,791 3.141381
32 1,024 5.656854 32,768 3.17482
33 1,089 5.744563 35,937 3.207534
34 1,156 5.830952 39,304 3.239612
35 1,225 5.916080 42,875 3.271066
36 1,296 6 46,656 3.301927
37 1,369 6.082763 50,653 3.332222
38 1,444 6164414 54,872 3.361975
39 1,521 6.244998 59,319 3.391211
40 1,600 6.324555 64,000 3.419952
41 1,681 6.403124 68,921 3.448217
42 1.764 6.480741 74,088 3.476027
43 1.849 6.557439 79,507 3.503398
44 1,936 6.633250 85,184 3.530348
45 2,025 6.708204 91,125 3.556893
46 2,116 6.782330 97,336 3.583048
47 2,209 6.855655 103,823 3.608826
48 2,304 6.928203 110,592 3.6324241
49 2,401 7 117,649 3.659306
50 2,500 7.071068 125,000 3.684031
51 2,601 7.141428 132,651 3.708430
52 2,704 7.211103 140,608 3.732511
53 2,809 7.280110 148,877 3.756286
54 2,916 7.348469 157,464 3.779763
55 3,025 7.416198 166,375 3.802952
56 3,136 7.483315 175,616 3.825862
57 3,249 7.549834 185,193 3.848501
58 3,364 7.615773 195,112 3.870877
59 3,481 7.681146 205,379 3.892996
60 3,600 7.745967 216,000 3.914868
61 3,721 7.810250 226,981 3.936497
62 3,844 7.874008 238,328 3.957892
63 3,969 7.937254 250,047 3.979057
64 4,096 8 262,144 4
65 4,225 8.062258 274,625 4.020726
66 6,356 8.124038 287,496 4.041240
67 4,489 8.185353 300,763 4.061548
68 4,624 8.246211 314,432 4.081655
69 4,761 8.306624 328,509 4.101566
70 4,900 8.366600 343,000 4.121285
71 5,041 8.426150 357,911 4.140818
72 5,184 8.485281 389,017 4.179339
73 5,329 8.544004 389,017 4.179339
74 5,476 8.602325 405,224 4.198336
75 5,625 8.660254 421,875 4.217163
76 5,776 8.17798 438,976 4.235824
77 5.929 8774964 456,533 4.254321
78 6,084 8.831761 474,552 4.272659
79 6,241 8.888194 493,039 4.290840
80 6,400 8.944272 512,000 4.308869
81 6,561 9 531,441 4.326749
82 6,724 9.055385 551,368 4.344481
83 6,889 9.110434 571,787 4.362071
84 7,056 9.165151 592,704 4.379519
85 7,225 9.219544 614,125 4.396830
86 7,396 9.273618 636,056 4.414005
87 7,569 9.327379 658,503 4.431048
88 7,744 9.380832 681,472 4.447960
89 7,821 8.433981 704,969 4.464745
90 8,100 9.486833 729,000 4.481405
91 8,281 9.539392 753,571 4.497941
92 8,464 9.591663 778,688 4.514357
93 8,649 9.643651 804,357 4.530655
94 8,836 9.695360 830,584 4.546836
95 9,025 9.746794 857,375 4.562903
96 9,216 9.797959 884,736 4.578857
97 9,409 9.848858 912,673 4.594701
98 9,604 9.899495 941,192 4.610436
99 9,801 9.949874 970,299 4.62065
100 10,000 10 1,000,000 4.641589

Contributors