# Cube

In arithmetic and algebra, the cube of a number n is its third power: the result of the number multiplied by itself twice. n3  = n x n x n. It is also the number multiplied by its square: n3 = n × n2. ## How to find Cube of any Number

To calculate  cube a number, just multiply it 3 times.

Example: What is the cube of 2?
Answer: The Cube of 2 is
= 2 X 2 X 2
= 8
Another Example,
What is the cube of 11?
Answer: The Cube of 11 is
= 11 X 11 X 11
= 1,331

Note: You Can Also Cube Negative Numbers
For Example:
−4 ×−4 × −4 = −64

## Cube Root

The cube root of a number is …
… a special value that when cubed gives the original number.

For Example The cube root of 125 is …
5, because when 5 is cubed to get 125.
To find the cube root of a number, you want to find some number that when multiplied by itself twice gives you the original number. In other words, to find the cube root of 8, you want to find the number that when multiplied by itself twice gives you 8. The cube root of 8, then, is 2, because 2 × 2 × 2 = 8.

## Cube Root Symbol

The symbol of Cube root is 3√

## Rules of Indices

2 × 24  = (2 × 2 × 2) × (2 × 2 × 2 × 2)

= 27
When dividing subtract the powers.

25 ÷ 22 = 2 x 2 x 2 x 2 x 2 over 2 x 2

= 2 × 2 × 2 (Cancelling two of the 2s)

= 23

When taking the power of a number already raised to a power, multiply the powers.

For example this is how to find the square of 23.

square of 23 = (23)2 = (2 × 2 × 2) × (2 × 2 × 2) = 26

Notice that the answer has an index of 6, which comes from multiplying the powers at the beginning (3 x 2). Here is another example.

(22)4 = (2 × 2) × (2 × 2) x (2 × 2) × (2 × 2) = 28

a) 3√729 = ?

b) 3√8 = ?

c) 3√8000 = ?

d) 3√125000 = ?

e) 3√970299 = ?

## Square and Cube Root Table

 No. Square Cube Square Root Cube Root 1 1 1 1.0000000 1.000000 2 4 8 1.4142136 1.259921 3 9 27 1.7320508 1.442250 4 16 64 2.0000000 1.537401 5 25 125 2.2360680 1.709976 6 36 216 2.4494897 1.817121 7 49 343 2.6457513 1.912931 8 64 512 2.8284271 2.000300 9 81 729 3.0000000 2.080084 10 100 1000 3.1622777 2.154435 11 121 1331 3.3166243 2.223930 12 144 1728 3.4641016 2.239429 13 169 2197 3.6055513 2351335 14 196 2744 3.7416574 2.410142 15 225 3375 3.8729833 2.466212 16 256 4096 4. 0000000 2.519842 17 239 4913 41231056 2.571282 18 324 5332 4.2426407 2.620741 19 361 6859 4.3588989 2.663402 20 400 8000 4.4721360 2.714418 21 441 9261 4.5825757 2.758924 22 484 10643 4.6904158 2.802039 23 529 12167 4.7953315 2.843367 24 576 13324 4.8989795 2.884499 25 625 15625 5.0000000 2.924018 26 676 17576 5.0990195 2.962496 27 729 19683 5.1961524 3.000000 28 784 21952 5 .2915028 3.036589 29 841 24389 5.3851648 3.072317 30 900 27000 5.4772256 3.107232 31 961 29791 55677644 3.141331 32 1024 32763 5.6568542 3.174802 33 1089 35937 5 7445626 3.207534 34 1156 39304 5.8399519 3.239612 35 1225 42875 5.9160798 3.271066 36 1296 46656 6 0000000 3.391927 37 1369 50653 6.0327625 3.332222 38 1444 54872 61644140 3.361975 39 1521 59319 6.2449980 3.391211 40 1600 64000 6.3245553 3.419952 41 1681 68921 6.4031242 3. 448217 42 1764 74038 6.4807407 3.476027 43 1849 79507 6.5574385 3.503398 44 1936 85184 6 6332496 3533348 45 2025 91125 6.7082039 3.556893 46 2116 97336 6.7823300 3.533348 47 2209 103323 6.8556546 3.608826 48 2304 110592 6.9232032 3.634241 49 2401 117649 7.0090030 3.659336 50 2500 125000 70710678 3.634031 51 2601 132651 7.1414284 3.708433 52 2704 140608 7.2111026 3.732511 53 2809 148877 7.2301099 3.756286 54 2916 157461 7.3484692 3.779763 55 3025 166375 7.4161985 3.302952 56 3136 175616 7.4833148 3.825862 57 3219 185193 7.5493344 3.343501 58 3364 195112 7.6157731 3.870877 59 3481 205379 7.6311457 3.892996 60 3600 216000 7.7459667 3.914868 61 3721 226981 7.8102497 3.936497 62 3344 233328 7.8740079 3..957891 63 3969 250047 7.9372539 3.979057 64 4096 262144 8. 0000000 4.000000 65 4225 274625 8.0622577 4.029726 66 4356 237496 8.1240384 4041240 67 4489 300763 8.1853523 4061548
 No. Square Cube Sq. Root Cube Root 68 4624 314432 8.2462113 4.081655 69 4761 328509 8.3066239 4 101566 70 4900 343000 8.3666003 4.121285 71 5041 357911 8.4261498 4.140818 72 5184 373248 8.4852814 4.160168 73 5329 389317 8.5440037 4.179339 74 5476 405224 8.6023253 4.193336 75 5625 421875 8.6602540 4 217163 76 5776 433976 8.7177979 4 235324 77 5929 456533 8.7749644 4.254321 78 6084 474552 8.8317609 4.272659 79 6241 493039 8.8881944 4.290840 83 6403 512000 8.9442719 4.308869 81 6561 531441 9.0000000 4.326749 82 6724 551368 9.0553851 4.344481 83 6889 571787 9.1104336 4.362071 84 7056 592704 9.1651514 4.379519 85 7225 614125 9.2195445 4.396830 86 7396 636056 9.2736185 4.414005 87 7569 653503 9.3273791 4.431048 88 7744 681472 9.3808315 4.447960 89 7921 704969 9.4339811 4.464745 90 8100 729300 9.4368330 4.481405 91 8281 753571 9.5393929 4.497941 92 8164 778688 9.5916630 4.514357 93 8649 804357 9 6436508 4.530655 94 8836 830584 9.6953597 4.516836 95 9025 857375 9.7467943 4.560903 96 9216 884736 9.7979590 4.578857 97 9409 912673 9.8483578 4.591701 98 9604 941192 9.8994949 4.610436 99 9301 970299 9.9498744 4.626065 100 10000 1000000 10.0000000 4 641589

## How To Calculate Cube Roots INSTANTLY!

These three step method is very good for calculating cube root of any number quickly

Step 1: See the Cubes of 0 to 9. But to memorize the cube up to 9 will be best if you want to check your answer in mind.

 Number Cube Last Digit 0 0 0 1 1 1 2 8 8 3 27 7 4 64 4 5 125 5 6 216 6 7 343 3 8 512 2 9 729 9

Step 2: Determine the Cube Root . Ignore the last three digits of the number called out by the Questioner and choose the memorized cube which is just lower (or equal) to the remaining number. The cube root of this is the first digit of your answer.
Now consider the last digit of the number called out by the Questioner. This will indicate the last digit of your answer. For example, if the last digit of the number called out is 3, then the last digit of the cube root is 7 (see the last digit values in the table above).

Step 3: Before you try this out on your friends, you should practice until you can calculate the cube root instantly and without error. If you can’t do this, then practice some more!

Some examples are in the table given below :

 Questioner Ignore last 3 Lower Cube First Digit Last Digit Cube Root 1728 1 1 1 2 12 21952 21 8 2 8 28 50653 50 27 3 7 37 117649 117 64 4 9 49 148877 148 125 5 3 53 216000 216 216 6 0 60 357911 357 343 7 1 71 636056 636 512 8 6 86 830584 830 729 9 4 94

If You want  to understand better and clear your doubts, watch the video below on How to Find Cube Root of any Number within Seconds.