12.2: Poderes y Raíces
- Page ID
- 114295
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Tabla B1
| \(n\) | \(n^{2}\) | \(\sqrt{n}\) | \(n^{3}\) | \(\sqrt[3]{n}\) |
|---|---|---|---|---|
| \ (n\) ">1 | \ (n^ {2}\) ">1 | \ (\ sqrt {n}\) ">1 | \ (n^ {3}\) ">1 | \ (\ sqrt [3] {n}\) ">1 |
| \ (n\) ">2 | \ (n^ {2}\) ">4 | \ (\ sqrt {n}\) ">1.414214 | \ (n^ {3}\) ">8 | \ (\ sqrt [3] {n}\) ">1.259921 |
| \ (n\) ">3 | \ (n^ {2}\) ">9 | \ (\ sqrt {n}\) ">1.732051 | \ (n^ {3}\) ">27 | \ (\ sqrt [3] {n}\) ">1.442250 |
| \ (n\) ">4 | \ (n^ {2}\) ">16 | \ (\ sqrt {n}\) ">2 | \ (n^ {3}\) ">64 | \ (\ sqrt [3] {n}\) ">1.587401 |
| \ (n\) ">5 | \ (n^ {2}\) ">25 | \ (\ sqrt {n}\) ">2.236068 | \ (n^ {3}\) ">125 | \ (\ sqrt [3] {n}\) ">1.709976 |
| \ (n\) ">6 | \ (n^ {2}\) ">36 | \ (\ sqrt {n}\) ">2.449490 | \ (n^ {3}\) ">216 | \ (\ sqrt [3] {n}\) ">1.817121 |
| \ (n\) ">7 | \ (n^ {2}\) ">49 | \ (\ sqrt {n}\) ">2.645751 | \ (n^ {3}\) ">343 | \ (\ sqrt [3] {n}\) ">1.912931 |
| \ (n\) ">8 | \ (n^ {2}\) ">64 | \ (\ sqrt {n}\) ">2.828427 | \ (n^ {3}\) ">512 | \ (\ sqrt [3] {n}\) ">2 |
| \ (n\) ">9 | \ (n^ {2}\) ">81 | \ (\ sqrt {n}\) ">3 | \ (n^ {3}\) ">729 | \ (\ sqrt [3] {n}\) ">2.080084 |
| \ (n\) ">10 | \ (n^ {2}\) ">100 | \ (\ sqrt {n}\) ">3.162278 | \ (n^ {3}\) ">1,000 | \ (\ sqrt [3] {n}\) ">2.154435 |
| \ (n\) ">11 | \ (n^ {2}\) ">121 | \ (\ sqrt {n}\) ">3316625 | \ (n^ {3}\) ">1,331 | \ (\ sqrt [3] {n}\) ">1.223980 |
| \ (n\) ">12 | \ (n^ {2}\) ">144 | \ (\ sqrt {n}\) ">3.464102 | \ (n^ {3}\) ">1,728 | \ (\ sqrt [3] {n}\) ">2.289428 |
| \ (n\) ">13 | \ (n^ {2}\) ">169 | \ (\ sqrt {n}\) ">3.605551 | \ (n^ {3}\) ">2.197 | \ (\ sqrt [3] {n}\) ">2.351335 |
| \ (n\) ">14 | \ (n^ {2}\) ">196 | \ (\ sqrt {n}\) ">3.741657 | \ (n^ {3}\) ">2.744 | \ (\ sqrt [3] {n}\) ">2.410142 |
| \ (n\) ">15 | \ (n^ {2}\) ">225 | \ (\ sqrt {n}\) ">3.872983 | \ (n^ {3}\) ">3.375 | \ (\ sqrt [3] {n}\) ">2.466212 |
| \ (n\) ">16 | \ (n^ {2}\) ">256 | \ (\ sqrt {n}\) ">4 | \ (n^ {3}\) ">4.096 | \ (\ sqrt [3] {n}\) ">2.519842 |
| \ (n\) ">17 | \ (n^ {2}\) ">289 | \ (\ sqrt {n}\) ">4.123106 | \ (n^ {3}\) ">4.913 | \ (\ sqrt [3] {n}\) ">2.571282 |
| \ (n\) ">18 | \ (n^ {2}\) ">324 | \ (\ sqrt {n}\) ">4.242641 | \ (n^ {3}\) ">5.832 | \ (\ sqrt [3] {n}\) ">2.620741 |
| \ (n\) ">19 | \ (n^ {2}\) ">361 | \ (\ sqrt {n}\) ">4.358899 | \ (n^ {3}\) ">6.859 | \ (\ sqrt [3] {n}\) ">2.668402 |
| \ (n\) ">20 | \ (n^ {2}\) ">400 | \ (\ sqrt {n}\) ">4.472136 | \ (n^ {3}\) ">8,000 | \ (\ sqrt [3] {n}\) ">2.714418 |
| \ (n\) ">21 | \ (n^ {2}\) ">441 | \ (\ sqrt {n}\) ">4.582576 | \ (n^ {3}\) ">9.261 | \ (\ sqrt [3] {n}\) ">2.758924 |
| \ (n\) ">22 | \ (n^ {2}\) ">484 | \ (\ sqrt {n}\) ">4.690416 | \ (n^ {3}\) ">10.648 | \ (\ sqrt [3] {n}\) ">2.802039 |
| \ (n\) ">23 | \ (n^ {2}\) ">529 | \ (\ sqrt {n}\) ">4.795832 | \ (n^ {3}\) ">12,167 | \ (\ sqrt [3] {n}\) ">2.843867 |
| \ (n\) ">24 | \ (n^ {2}\) ">576 | \ (\ sqrt {n}\) ">4.898979 | \ (n^ {3}\) ">13,824 | \ (\ sqrt [3] {n}\) ">2.884499 |
| \ (n\) ">25 | \ (n^ {2}\) ">625 | \ (\ sqrt {n}\) ">5 | \ (n^ {3}\) ">15,625 | \ (\ sqrt [3] {n}\) ">2.924018 |
| \ (n\) ">26 | \ (n^ {2}\) ">676 | \ (\ sqrt {n}\) ">5.099020 | \ (n^ {3}\) ">17.576 | \ (\ sqrt [3] {n}\) ">2.962496 |
| \ (n\) ">27 | \ (n^ {2}\) ">729 | \ (\ sqrt {n}\) ">5.196152 | \ (n^ {3}\) ">19.683 | \ (\ sqrt [3] {n}\) ">3 |
| \ (n\) ">28 | \ (n^ {2}\) ">784 | \ (\ sqrt {n}\) ">5.291503 | \ (n^ {3}\) ">21.952 | \ (\ sqrt [3] {n}\) ">3.036589 |
| \ (n\) ">29 | \ (n^ {2}\) ">841 | \ (\ sqrt {n}\) ">5.385165 | \ (n^ {3}\) ">24.389 | \ (\ sqrt [3] {n}\) ">3.072317 |
| \ (n\) ">30 | \ (n^ {2}\) ">900 | \ (\ sqrt {n}\) ">5.477226 | \ (n^ {3}\) ">27,000 | \ (\ sqrt [3] {n}\) ">3.107233 |
| \ (n\) ">31 | \ (n^ {2}\) ">961 | \ (\ sqrt {n}\) ">5.567764 | \ (n^ {3}\) ">29.791 | \ (\ sqrt [3] {n}\) ">3.141381 |
| \ (n\) ">32 | \ (n^ {2}\) ">1,024 | \ (\ sqrt {n}\) ">5.656854 | \ (n^ {3}\) ">32.768 | \ (\ sqrt [3] {n}\) ">3.17482 |
| \ (n\) ">33 | \ (n^ {2}\) ">1,089 | \ (\ sqrt {n}\) ">5.744563 | \ (n^ {3}\) ">35.937 | \ (\ sqrt [3] {n}\) ">3.207534 |
| \ (n\) ">34 | \ (n^ {2}\) ">1.156 | \ (\ sqrt {n}\) ">5.830952 | \ (n^ {3}\) ">39.304 | \ (\ sqrt [3] {n}\) ">3.239612 |
| \ (n\) ">35 | \ (n^ {2}\) ">1,225 | \ (\ sqrt {n}\) ">5.916080 | \ (n^ {3}\) ">42.875 | \ (\ sqrt [3] {n}\) ">3.271066 |
| \ (n\) ">36 | \ (n^ {2}\) ">1,296 | \ (\ sqrt {n}\) ">6 | \ (n^ {3}\) ">46.656 | \ (\ sqrt [3] {n}\) ">3.301927 |
| \ (n\) ">37 | \ (n^ {2}\) ">1,369 | \ (\ sqrt {n}\) ">6.082763 | \ (n^ {3}\) ">50,653 | \ (\ sqrt [3] {n}\) ">3.332222 |
| \ (n\) ">38 | \ (n^ {2}\) ">1,444 | \ (\ sqrt {n}\) ">6164414 | \ (n^ {3}\) ">54.872 | \ (\ sqrt [3] {n}\) ">3.361975 |
| \ (n\) ">39 | \ (n^ {2}\) ">1,521 | \ (\ sqrt {n}\) ">6.244998 | \ (n^ {3}\) ">59,319 | \ (\ sqrt [3] {n}\) ">3.391211 |
| \ (n\) ">40 | \ (n^ {2}\) ">1,600 | \ (\ sqrt {n}\) ">6.324555 | \ (n^ {3}\) ">64.000 | \ (\ sqrt [3] {n}\) ">3.419952 |
| \ (n\) ">41 | \ (n^ {2}\) ">1,681 | \ (\ sqrt {n}\) ">6.403124 | \ (n^ {3}\) ">68,921 | \ (\ sqrt [3] {n}\) ">3.448217 |
| \ (n\) ">42 | \ (n^ {2}\) ">1.764 | \ (\ sqrt {n}\) ">6.480741 | \ (n^ {3}\) ">74.088 | \ (\ sqrt [3] {n}\) ">3.476027 |
| \ (n\) ">43 | \ (n^ {2}\) ">1.849 | \ (\ sqrt {n}\) ">6.557439 | \ (n^ {3}\) ">79,507 | \ (\ sqrt [3] {n}\) ">3.503398 |
| \ (n\) ">44 | \ (n^ {2}\) ">1,936 | \ (\ sqrt {n}\) ">6.633250 | \ (n^ {3}\) ">85,184 | \ (\ sqrt [3] {n}\) ">3.530348 |
| \ (n\) ">45 | \ (n^ {2}\) ">2,025 | \ (\ sqrt {n}\) ">6.708204 | \ (n^ {3}\) ">91,125 | \ (\ sqrt [3] {n}\) ">3.556893 |
| \ (n\) ">46 | \ (n^ {2}\) ">2,116 | \ (\ sqrt {n}\) ">6.782330 | \ (n^ {3}\) ">97,336 | \ (\ sqrt [3] {n}\) ">3.583048 |
| \ (n\) ">47 | \ (n^ {2}\) ">2.209 | \ (\ sqrt {n}\) ">6.855655 | \ (n^ {3}\) ">103,823 | \ (\ sqrt [3] {n}\) ">3.608826 |
| \ (n\) ">48 | \ (n^ {2}\) ">2.304 | \ (\ sqrt {n}\) ">6.928203 | \ (n^ {3}\) ">110,592 | \ (\ sqrt [3] {n}\) ">3.6324241 |
| \ (n\) ">49 | \ (n^ {2}\) ">2.401 | \ (\ sqrt {n}\) ">7 | \ (n^ {3}\) ">117.649 | \ (\ sqrt [3] {n}\) ">3.659306 |
| \ (n\) ">50 | \ (n^ {2}\) ">2,500 | \ (\ sqrt {n}\) ">7.071068 | \ (n^ {3}\) ">125.000 | \ (\ sqrt [3] {n}\) ">3.684031 |
| \ (n\) ">51 | \ (n^ {2}\) ">2.601 | \ (\ sqrt {n}\) ">7.141428 | \ (n^ {3}\) ">132.651 | \ (\ sqrt [3] {n}\) ">3.708430 |
| \ (n\) ">52 | \ (n^ {2}\) ">2.704 | \ (\ sqrt {n}\) ">7.211103 | \ (n^ {3}\) ">140.608 | \ (\ sqrt [3] {n}\) ">3.732511 |
| \ (n\) ">53 | \ (n^ {2}\) ">2.809 | \ (\ sqrt {n}\) ">7.280110 | \ (n^ {3}\) ">148.877 | \ (\ sqrt [3] {n}\) ">3.756286 |
| \ (n\) ">54 | \ (n^ {2}\) ">2.916 | \ (\ sqrt {n}\) ">7.348469 | \ (n^ {3}\) ">157.464 | \ (\ sqrt [3] {n}\) ">3.779763 |
| \ (n\) ">55 | \ (n^ {2}\) ">3,025 | \ (\ sqrt {n}\) ">7.416198 | \ (n^ {3}\) ">166.375 | \ (\ sqrt [3] {n}\) ">3.802952 |
| \ (n\) ">56 | \ (n^ {2}\) ">3,136 | \ (\ sqrt {n}\) ">7.483315 | \ (n^ {3}\) ">175.616 | \ (\ sqrt [3] {n}\) ">3.825862 |
| \ (n\) ">57 | \ (n^ {2}\) ">3,249 | \ (\ sqrt {n}\) ">7.549834 | \ (n^ {3}\) ">185.193 | \ (\ sqrt [3] {n}\) ">3.848501 |
| \ (n\) ">58 | \ (n^ {2}\) ">3.364 | \ (\ sqrt {n}\) ">7.615773 | \ (n^ {3}\) ">195,112 | \ (\ sqrt [3] {n}\) ">3.870877 |
| \ (n\) ">59 | \ (n^ {2}\) ">3.481 | \ (\ sqrt {n}\) ">7.681146 | \ (n^ {3}\) ">205.379 | \ (\ sqrt [3] {n}\) ">3.892996 |
| \ (n\) ">60 | \ (n^ {2}\) ">3.600 | \ (\ sqrt {n}\) ">7.745967 | \ (n^ {3}\) ">216,000 | \ (\ sqrt [3] {n}\) ">3.914868 |
| \ (n\) ">61 | \ (n^ {2}\) ">3.721 | \ (\ sqrt {n}\) ">7.810250 | \ (n^ {3}\) ">226.981 | \ (\ sqrt [3] {n}\) ">3.936497 |
| \ (n\) ">62 | \ (n^ {2}\) ">3,844 | \ (\ sqrt {n}\) ">7.874008 | \ (n^ {3}\) ">238.328 | \ (\ sqrt [3] {n}\) ">3.957892 |
| \ (n\) ">63 | \ (n^ {2}\) ">3.969 | \ (\ sqrt {n}\) ">7.937254 | \ (n^ {3}\) ">250.047 | \ (\ sqrt [3] {n}\) ">3.979057 |
| \ (n\) ">64 | \ (n^ {2}\) ">4.096 | \ (\ sqrt {n}\) ">8 | \ (n^ {3}\) ">262,144 | \ (\ sqrt [3] {n}\) ">4 |
| \ (n\) ">65 | \ (n^ {2}\) ">4.225 | \ (\ sqrt {n}\) ">8.062258 | \ (n^ {3}\) ">274.625 | \ (\ sqrt [3] {n}\) ">4.020726 |
| \ (n\) ">66 | \ (n^ {2}\) ">6.356 | \ (\ sqrt {n}\) ">8.124038 | \ (n^ {3}\) ">287.496 | \ (\ sqrt [3] {n}\) ">4.041240 |
| \ (n\) ">67 | \ (n^ {2}\) ">4.489 | \ (\ sqrt {n}\) ">8.185353 | \ (n^ {3}\) ">300,763 | \ (\ sqrt [3] {n}\) ">4.061548 |
| \ (n\) ">68 | \ (n^ {2}\) ">4.624 | \ (\ sqrt {n}\) ">8.246211 | \ (n^ {3}\) ">314,432 | \ (\ sqrt [3] {n}\) ">4.081655 |
| \ (n\) ">69 | \ (n^ {2}\) ">4.761 | \ (\ sqrt {n}\) ">8.306624 | \ (n^ {3}\) ">328.509 | \ (\ sqrt [3] {n}\) ">4.101566 |
| \ (n\) ">70 | \ (n^ {2}\) ">4.900 | \ (\ sqrt {n}\) ">8.366600 | \ (n^ {3}\) ">343,000 | \ (\ sqrt [3] {n}\) ">4.121285 |
| \ (n\) ">71 | \ (n^ {2}\) ">5.041 | \ (\ sqrt {n}\) ">8.426150 | \ (n^ {3}\) ">357.911 | \ (\ sqrt [3] {n}\) ">4.140818 |
| \ (n\) ">72 | \ (n^ {2}\) ">5.184 | \ (\ sqrt {n}\) ">8.485281 | \ (n^ {3}\) ">389.017 | \ (\ sqrt [3] {n}\) ">4.179339 |
| \ (n\) ">73 | \ (n^ {2}\) ">5.329 | \ (\ sqrt {n}\) ">8.544004 | \ (n^ {3}\) ">389.017 | \ (\ sqrt [3] {n}\) ">4.179339 |
| \ (n\) ">74 | \ (n^ {2}\) ">5.476 | \ (\ sqrt {n}\) ">8.602325 | \ (n^ {3}\) ">405,224 | \ (\ sqrt [3] {n}\) ">4.198336 |
| \ (n\) ">75 | \ (n^ {2}\) ">5.625 | \ (\ sqrt {n}\) ">8.660254 | \ (n^ {3}\) ">421,875 | \ (\ sqrt [3] {n}\) ">4.217163 |
| \ (n\) ">76 | \ (n^ {2}\) ">5.776 | \ (\ sqrt {n}\) ">8.17798 | \ (n^ {3}\) ">438.976 | \ (\ sqrt [3] {n}\) ">4.235824 |
| \ (n\) ">77 | \ (n^ {2}\) ">5.929 | \ (\ sqrt {n}\) ">8774964 | \ (n^ {3}\) ">456.533 | \ (\ sqrt [3] {n}\) ">4.254321 |
| \ (n\) ">78 | \ (n^ {2}\) ">6.084 | \ (\ sqrt {n}\) ">8.831761 | \ (n^ {3}\) ">474.552 | \ (\ sqrt [3] {n}\) ">4.272659 |
| \ (n\) ">79 | \ (n^ {2}\) ">6.241 | \ (\ sqrt {n}\) ">8.888194 | \ (n^ {3}\) ">493,039 | \ (\ sqrt [3] {n}\) ">4.290840 |
| \ (n\) ">80 | \ (n^ {2}\) ">6.400 | \ (\ sqrt {n}\) ">8.944272 | \ (n^ {3}\) ">512,000 | \ (\ sqrt [3] {n}\) ">4.308869 |
| \ (n\) ">81 | \ (n^ {2}\) ">6.561 | \ (\ sqrt {n}\) ">9 | \ (n^ {3}\) ">531.441 | \ (\ sqrt [3] {n}\) ">4.326749 |
| \ (n\) ">82 | \ (n^ {2}\) ">6.724 | \ (\ sqrt {n}\) ">9.055385 | \ (n^ {3}\) ">551,368 | \ (\ sqrt [3] {n}\) ">4.344481 |
| \ (n\) ">83 | \ (n^ {2}\) ">6.889 | \ (\ sqrt {n}\) ">9.110434 | \ (n^ {3}\) ">571,787 | \ (\ sqrt [3] {n}\) ">4.362071 |
| \ (n\) ">84 | \ (n^ {2}\) ">7.056 | \ (\ sqrt {n}\) ">9.165151 | \ (n^ {3}\) ">592.704 | \ (\ sqrt [3] {n}\) ">4.379519 |
| \ (n\) ">85 | \ (n^ {2}\) ">7,225 | \ (\ sqrt {n}\) ">9.219544 | \ (n^ {3}\) ">614,125 | \ (\ sqrt [3] {n}\) ">4.396830 |
| \ (n\) ">86 | \ (n^ {2}\) ">7.396 | \ (\ sqrt {n}\) ">9.273618 | \ (n^ {3}\) ">636.056 | \ (\ sqrt [3] {n}\) ">4.414005 |
| \ (n\) ">87 | \ (n^ {2}\) ">7.569 | \ (\ sqrt {n}\) ">9.327379 | \ (n^ {3}\) ">658,503 | \ (\ sqrt [3] {n}\) ">4.431048 |
| \ (n\) ">88 | \ (n^ {2}\) ">7.744 | \ (\ sqrt {n}\) ">9.380832 | \ (n^ {3}\) ">681.472 | \ (\ sqrt [3] {n}\) ">4.447960 |
| \ (n\) ">89 | \ (n^ {2}\) ">7.821 | \ (\ sqrt {n}\) ">8.433981 | \ (n^ {3}\) ">704.969 | \ (\ sqrt [3] {n}\) ">4.464745 |
| \ (n\) ">90 | \ (n^ {2}\) ">8.100 | \ (\ sqrt {n}\) ">9.486833 | \ (n^ {3}\) ">729,000 | \ (\ sqrt [3] {n}\) ">4.481405 |
| \ (n\) ">91 | \ (n^ {2}\) ">8.281 | \ (\ sqrt {n}\) ">9.539392 | \ (n^ {3}\) ">753.571 | \ (\ sqrt [3] {n}\) ">4.497941 |
| \ (n\) ">92 | \ (n^ {2}\) ">8.464 | \ (\ sqrt {n}\) ">9.591663 | \ (n^ {3}\) ">778.688 | \ (\ sqrt [3] {n}\) ">4.514357 |
| \ (n\) ">93 | \ (n^ {2}\) ">8.649 | \ (\ sqrt {n}\) ">9.643651 | \ (n^ {3}\) ">804.357 | \ (\ sqrt [3] {n}\) ">4.530655 |
| \ (n\) ">94 | \ (n^ {2}\) ">8.836 | \ (\ sqrt {n}\) ">9.695360 | \ (n^ {3}\) ">830.584 | \ (\ sqrt [3] {n}\) ">4.546836 |
| \ (n\) ">95 | \ (n^ {2}\) ">9.025 | \ (\ sqrt {n}\) ">9.746794 | \ (n^ {3}\) ">857.375 | \ (\ sqrt [3] {n}\) ">4.562903 |
| \ (n\) ">96 | \ (n^ {2}\) ">9,216 | \ (\ sqrt {n}\) ">9.797959 | \ (n^ {3}\) ">884.736 | \ (\ sqrt [3] {n}\) ">4.578857 |
| \ (n\) ">97 | \ (n^ {2}\) ">9.409 | \ (\ sqrt {n}\) ">9.848858 | \ (n^ {3}\) ">912.673 | \ (\ sqrt [3] {n}\) ">4.594701 |
| \ (n\) ">98 | \ (n^ {2}\) ">9.604 | \ (\ sqrt {n}\) ">9.899495 | \ (n^ {3}\) ">941.192 | \ (\ sqrt [3] {n}\) ">4.610436 |
| \ (n\) ">99 | \ (n^ {2}\) ">9.801 | \ (\ sqrt {n}\) ">9.949874 | \ (n^ {3}\) ">970,299 | \ (\ sqrt [3] {n}\) ">4.62065 |
| \ (n\) ">100 | \ (n^ {2}\) ">10,000 | \ (\ sqrt {n}\) ">10 | \ (n^ {3}\) ">1.000.000 | \ (\ sqrt [3] {n}\) ">4.641589 |