12.2: Powers and Roots

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

Table B1