What Is A Perfect Cube

Perfect Cube

The perfect cube is the outcome of multiplying the same integer three times. Multiplying the number 4 three times, for example, yields 64. As a event, the number 64 is a perfect cube. Perfect cube = number x number x number. If a number tin be broken down into a product of the same three numbers, it is said to exist a perfect cube.

Cube

Definition of a Perfect Cube

A perfect cube is the product of three identical numbers. To see if a number 'N' is a perfect cube, multiply it by itself iii times and see if the outcome is the number 'N'. If you answered yes, you have a perfect cube. A perfect cube has the numbers 1, 8, 27, and 64 as examples. A perfect square tin be made by multiplying ii numbers together. It'due south not the aforementioned as a flawless cube. Both positive and negative integers can be used to brand perfect cubes. For case, -64 is a perfect cube since it is the effect of multiplying -iv three times.

Root Cube

When we say a number has been cubed, we indicate that it has been multiplied three times. The process of cubing a number is reversed with cube root. When the number 5 is cubed, for example, we obtain 5 x 5 x 5, which equals 125. The number 125 has a cube root of five. This is considering multiplying the number 5 three times yields 125. Cube root is represented by the symbol: It's the same as the square root sign, except with the addition of a '3' to indicate that it's a cube root. The cube root of an integer can be represented in exponent form equally (number)ane/3.

Number	Multiplication Fact	Perfect Cube
1	one × 1 × 1	1
ii	2 × 2 × 2	8
three	iii × 3 × iii	27
4	iv × iv × 4	64
v	five × 5 × 5	125
6	6 × 6 × half dozen	216
vii	vii × 7 × 7	343
8	8 × viii × 8	512
9	9 × ix × 9	729
10	10 × 10 × 10	1000
11	11 × 11 × eleven	1331
12	12 × 12 × 12	1728
13	13 × 13 × 13	2197
xiv	14 × 14 × fourteen	2744
15	15 × xv × xv	3375
16	xvi × 16 × sixteen	4096
17	17 × 17 × 17	4913
18	18 × eighteen × 18	5832
19	xix × 19 × 19	6859
xx	20 × 20 × 20	8000
21	21 × 21 × 21	9261
22	22 × 22 × 22	10648
23	23 × 23 × 23	12167
24	24 × 24 × 24	13824
25	25 × 25 × 25	15625
26	26 × 26 × 26	17576
27	27 × 27 × 27	19683
28	28 × 28 × 28	21952
29	29 × 29 × 29	24389
30	30 × 30 × xxx	27000
31	31 × 31 × 31	29791
32	32 × 32 × 32	32768
33	33 × 33 × 33	35937
34	34 × 34 × 34	39304
35	35 × 35 × 35	42875
36	36 × 36 × 36	46656
37	37 × 37 × 37	50653
28	38 × 38 × 38	54872
39	39 × 39 × 39	59319
40	forty × twoscore × twoscore	64000
41	41 × 41 × 41	68921
42	42 × 42 × 42	74088
43	43 × 43 × 43	79507
44	44 × 44 × 44	85184
45	45 × 45 × 45	91125
46	46 × 46 × 46	97336
47	47 × 47 × 47	103823
48	48 × 48 × 48	110592
49	49 × 49 × 49	117649
50	50 × 50 × 50	125000

There is a method for determining whether or not larger numbers are perfect cubes. To check, add together upward all of the digits in the number and determine if the result is 0, 1, eight, or 9. If it's any of these, it may be a perfect cube, although that isn't ever the case. To decide if it is a perfect cube, we must repeat the prime number factorization procedure described earlier. This is a method for determining if a number is a perfect cube or not, notwithstanding information technology is not always guaranteed.

This technique is utilized because allow's assume nosotros're given a number, like 8768, and we're non sure if it'south a perfect cube or not. And so, we calculate the sum of this number'south digits and see if it's 0, 1, eight, or nine. If the number isn't one of these four, we don't need to factorize it to see if information technology's a perfect cube. In other words, if the sum is not equal to 0, i, viii, or 9, this technique just bypasses the prime factorization procedure. In this example, the full of the digits of the integers 8768 equals 29, the sum of 2 and ix is eleven, and i + 1 = 2. As a result, the reply isn't 0, one, 8, or 9. As a effect, it's like shooting fish in a barrel to deduce that 8768 isn't a perfect cube.