12.2: Powers and Roots
- Page ID
- 7303
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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 and Attributions
Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/fd53eae1-fa2...49835c3c@5.191."