12.2: Powers and Roots

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May 28, 2023
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- 12.1: Cumulative Review
- 12.3: Geometric Formulas

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$n$	$n^{2}$	$\sqrt{n}$	$n^{3}$	$\sqrt[3]{n}$
$1$	$1$	$1$	$1$	$1$
$2$	$4$	$1.414214$	$8$	$1.259921$
$3$	$9$	$1.732051$	$27$	$1.442250$
$4$	$16$	$2$	$64$	$1.587401$
$5$	$25$	$2.236068$	$125$	$1.709976$
$6$	$36$	$2.449490$	$216$	$1.817121$
$7$	$49$	$2.645751$	$343$	$1.912931$
$8$	$64$	$2.828427$	$512$	$2$
$9$	$81$	$3$	$729$	$2.080084$
$10$	$100$	$3.162278$	$1,000$	$2.154435$
$11$	$121$	$3.316625$	$1,331$	$2.223980$
$12$	$144$	$3.464102$	$1,728$	$2.289428$
$13$	$169$	$3.605551$	$2,197$	$2.351335$
$14$	$196$	$3.741657$	$2,744$	$2.410142$
$15$	$225$	$3.872983$	$3,375$	$2.466212$
$16$	$256$	$4$	$4,096$	$2.519842$
$17$	$289$	$4.123106$	$4,913$	$2.571282$
$18$	$324$	$4.242641$	$5,832$	$2.620741$
$19$	$361$	$4.358899$	$6,859$	$2.668402$
$20$	$400$	$4.472136$	$8,000$	$2.714418$
$21$	$441$	$4.582576$	$9,261$	$2.758924$
$22$	$484$	$4.690416$	$10,648$	$2.802039$
$23$	$529$	$4.795832$	$12,167$	$2.843867$
$24$	$576$	$4.898979$	$13,824$	$2.884499$
$25$	$625$	$5$	$15,625$	$2.924018$
$26$	$676$	$5.099020$	$17,576$	$2.962496$
$27$	$729$	$5.196152$	$19,683$	$3$
$28$	$784$	$5.291503$	$21,952$	$3.036589$
$29$	$841$	$5.385165$	$24,389$	$3.072317$
$30$	$900$	$5.477226$	$27,000$	$3.107233$
$31$	$961$	$5.567764$	$29,791$	$3.141381$
$32$	$1,024$	$5.656854$	$32,768$	$3.174802$
$33$	$1,089$	$5.744563$	$35,937$	$3.207534$
$34$	$1,156$	$5.830952$	$39,304$	$3.239612$
$35$	$1,225$	$5.916080$	$42,875$	$3.271066$
$36$	$1,296$	$6$	$46,656$	$3.301927$
$37$	$1,369$	$6.082763$	$50653$	$3.332222$
$38$	$1,444$	$6.164414$	$54,872$	$3.361975$
$39$	$1,521$	$6.244998$	$59,319$	$3.391211$
$40$	$1,600$	$6.324555$	$64,000$	$3.419952$
$41$	$1,681$	$6.403124$	$68,921$	$3.448217$
$42$	$1,764$	$6.480741$	$74,088$	$3.476027$
$43$	$1,849$	$6.557439$	$79,507$	$3.503398$
$44$	$1,936$	$6.633250$	$85,184$	$3.530348$
$45$	$2,025$	$6.708204$	$91,125$	$3.556893$
$46$	$2,116$	$6.782330$	$97,336$	$3.583048$
$47$	$2,209$	$6.855655$	$103,823$	$3.608826$
$48$	$2,304$	$6.928203$	$110,592$	$3.634241$
$49$	$2,401$	$7$	$117,649$	$3.659306$
$50$	$2,500$	$7.071068$	$125,000$	$3.684031$
$51$	$2,601$	$7.141428$	$132,651$	$3.708430$
$52$	$2,704$	$7.211103$	$140,608$	$3.732511$
$53$	$2,809$	$7.280110$	$148,877$	$3.756286$
$54$	$2,916$	$7.348469$	$157,464$	$3.779763$
$55$	$3,025$	$7.416198$	$166,375$	$3.802952$
$56$	$3,136$	$7.483315$	$175,616$	$3.825862$
$57$	$3,249$	$7.549834$	$185,193$	$3.848501$
$58$	$3,364$	$7.615773$	$195,112$	$3.870877$
$59$	$3,481$	$7.681146$	$205,379$	$3.892996$
$60$	$3,600$	$7.745967$	$216,000$	$3.914868$
$61$	$3,721$	$7.810250$	$226,981$	$3.936497$
$62$	$3,844$	$7.874008$	$238,328$	$3.957892$
$63$	$3,969$	$7.937254$	$250,047$	$3.979057$
$64$	$4,096$	$8$	$262,144$	$4$
$65$	$4,225$	$8.062258$	$274,625$	$4.020726$
$66$	$4,356$	$8.124038$	$287,496$	$4.041240$
$67$	$4,489$	$8.185353$	$300,763$	$4.061548$
$68$	$4,624$	$8.246211$	$314,432$	$4.081655$
$69$	$4,761$	$8.306624$	$328,509$	$4.101566$
$70$	$4,900$	$8.366600$	$343,000$	$4.121285$
$71$	$5,041$	$8.426150$	$357,911$	$4.140818$
$72$	$5,184$	$8.485281$	$373,248$	$4.160168$
$73$	$5,329$	$8.544004$	$389,017$	$4.179339$
$74$	$5,476$	$8.602325$	$405,224$	$4.198336$
$75$	$5,625$	$8.660254$	$421,875$	$4.217163$
$76$	$5,776$	$8.717798$	$438,976$	$4.235824$
$77$	$5,929$	$8.774964$	$456,533$	$4.254321$
$78$	$6,084$	$8.831761$	$474,552$	$4.272659$
$79$	$6,241$	$8.888194$	$493,039$	$4.290840$
$80$	$6,400$	$8.944272$	$512,000$	$4.308869$
$81$	$6,561$	$9$	$531,441$	$4.326749$
$82$	$6,724$	$9.055385$	$551,368$	$4.344481$
$83$	$6,889$	$9.110434$	$571,787$	$4.362071$
$84$	$7,056$	$9.165151$	$592,704$	$4.379519$
$85$	$7,225$	$9.219544$	$614,125$	$4.396830$
$86$	$7,396$	$9.273618$	$636,056$	$4.414005$
$87$	$7,569$	$9.327379$	$658,503$	$4.431048$
$88$	$7,744$	$9.380832$	$681,472$	$4.447960$
$89$	$7,921$	$9.433981$	$704,969$	$4.464745$
$90$	$8,100$	$9.486833$	$729,000$	$4.481405$
$91$	$8,281$	$9.539392$	$753,571$	$4.497941$
$92$	$8,464$	$9.591663$	$778,688$	$4.514357$
$93$	$8,649$	$9.643651$	$804,357$	$4.530655$
$94$	$8,836$	$9.695360$	$830,584$	$4.546836$
$95$	$9,025$	$9.746794$	$857,375$	$4.562903$
$96$	$9,216$	$9.797959$	$884,736$	$4.578857$
$97$	$9,409$	$9.848858$	$912,673$	$4.594701$
$98$	$9,604$	$9.899495$	$941,192$	$4.610436$
$99$	$9,801$	$9.949874$	$970,299$	$4.626065$
$100$	$10,000$	$10$	$1,000,000$	$4.641589$

Table B1

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