Is 8 A Perfect Cube

A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If 10 is a perfect cube of y, so x = y³. Therefore, if we take the cube root of a perfect cube, we go a natural number and not a fraction. Hence, ³ √x = y. For instance, 8 is a perfect cube because³√viii = 2. The major application of cubes tin can be seen in geometry while determining the volume of a cube (a 3d shape). Permit us learn here the definition, list of perfect cubes, applications with examples.

What are Perfect Cubes?

Perfect cubes are the numbers that are the triple production of the same number. In other words, a perfect cube is a value that is the issue of three times multiplication of a whole number to itself. A perfect cube is a number, that can be written every bit three times the product of the same number.

The cube root of a perfect cube always results in a whole number. But we can discover cubes of any number whether information technology is an integer or a fraction. For example, the cube of 0.5 is:

0.5 × 0.v × 0.five = 0.125

Let us see the list of perfect cubes in the next section.

List of Perfect Cubes i to 50

Number (10)	Multiplied Iii times by itself	Cubes (ten³)
1	1× ane× i	1
2	2× 2× 2	viii
iii	3× three× 3	27
four	4× four× 4	64
v	5× five× five	125
vi	half dozen× 6× 6	216
7	vii× seven× 7	343
eight	eight× viii× 8	512
ix	9× 9× 9	729
ten	ten× 10× 10	yard
11	xi× eleven× 11	1331
12	12× 12× 12	1728
13	13× xiii× 13	2197
fourteen	14× fourteen× xiv	2744
15	15× 15× 15	3375
16	16× 16× sixteen	4096
17	17× 17× 17	4913
18	18× 18× 18	5832
19	19× xix× 19	6859
20	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	xxx× 30× 30	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
38	38× 38× 38	54872
39	39× 39× 39	59319
40	twoscore× twoscore× 40	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

How to Find a Perfect Cube?

Every number can be expressed every bit the product of the ability of its Prime factors. If the power of all the Prime factors is in the multiple of three, then the number is said to be a perfect cube.

1) xv = 3 × five

15³= fifteen × 15 × 15 = iii × five × 3 × v × 3 × 5 = 3³× 5³

2) 18 = 2 × 3 × iii

18³ = 18 × 18 × 18 = 2 × 3 × 3 × two × iii × iii × 2 × 3 × 3 = 2ⁱⁱⁱ × 3³× 3ⁱⁱⁱ

From the above examples, we can observe that each prime cistron of a number appears three times in the prime factorization of its cube.

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Solved Examples on Perfect Cubes

Question 1: Is the number 600 a perfect cube?

Allow us write downwardly, stating the prime factors of the number 600.

\(\brainstorm{array}{fifty}600 = 2 \times ii\times two \times three \times 5 \times 5 = ii^{3}.3.5^{2} \end{array} \)

The number 600 is not a perfect cube as all the prime factors is not a multiple of three.

Question 2: What should exist multiplied to the number 120 to make information technology a perfect cube?

\(\brainstorm{array}{l} Factors\ of\ 120 = ii \times 2 \times 2 \times 3 \times five = 2^{three}. 3.v\terminate{array} \)

The factor two occurs thrice, iii and 5 occurs just one time. So in guild to make it a perfect cube we have to multiply 120 with a square of 3 and 5.

Therefore, 120 × 3 × 3 × 5 × 5 =27000

The number 27000 is the required perfect cube.

Application of Perfect Cubes

A cube is a three-dimensional effigy which has all the edges of equal length. The volume of a cube is given by the product of its dimensions. For example, for a cube of edge length 'a' units, the book of the cube is given by "a × a × a"which is equal to aⁱⁱⁱcubic unit. Similarly, we tin can summate the perfect cube of various numbers.

Perfect Cube

Illustration: Make up one's mind the volume of a cube with an edge length of seven cm.

Solution: The side of the cube is 7 cm.

Volume = side × side × side = seven × seven × 7 = 343 cm³.

The numbers such as 1, viii, 27, 64, etc. are known as perfect cubes or cube numbers.

When a cube is broken or cutting, full volume still remains the same. Hence, we can discover that to construct a cube of edge length '2a' with cubes of edge length 'a' nosotros need to have 8 cubes of edge length a.

This commodity explains perfect cubes and the method of their calculation. To learn more about other topics download BYJU'S – The Learning App and picket interactive videos. Too, have complimentary tests to practice for exams.

Oft Asked Questions on Perfect Cubes

What is a perfect cube?

When a natural number is multiplied three times to itself, and then the resulting value is called perfect cube.

What is the perfect cube of 100?

The prefect cube of 100 is 100 x 100 ten 100 = meg

What are get-go 10 perfect cube numbers?

The get-go x cube numbers are 1, viii, 27, 64, 125, 216, 343, 512, 729 and grand.

Which are the perfect cubes among these: 27, 9, 400?

27 is the perfect cube. Since 3 x 3 x three = 3³ = 27
nine and 400 are the perfect squares. 3 x 3 = nine and 20 x xx = 400

What is the cube 30?