Is 4 A Perfect Cube

A perfect cube of a number is a number that is equal to the number, multiplied past itself, three times. If x is a perfect cube of y, and then x = y³. Therefore, if we have the cube root of a perfect cube, we get a natural number and not a fraction. Hence, ³ √x = y. For example, 8 is a perfect cube because³√8 = 2. The major application of cubes tin can be seen in geometry while determining the book of a cube (a 3d shape). Permit united states acquire here the definition, list of perfect cubes, applications with examples.

What are Perfect Cubes?

Perfect cubes are the numbers that are the triple product of the aforementioned number. In other words, a perfect cube is a value that is the effect of iii times multiplication of a whole number to itself. A perfect cube is a number, that tin can be written as three times the product of the same number.

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

0.5 × 0.5 × 0.5 = 0.125

Allow u.s. run into the list of perfect cubes in the adjacent section.

List of Perfect Cubes ane to 50

Number (x)	Multiplied Three times past itself	Cubes (x³)
1	one× 1× ane	one
2	2× 2× 2	8
3	3× iii× three	27
4	4× 4× iv	64
5	5× v× 5	125
vi	6× vi× 6	216
7	seven× 7× 7	343
8	viii× viii× 8	512
9	9× nine× 9	729
x	10× 10× x	thousand
xi	11× 11× xi	1331
12	12× 12× 12	1728
13	thirteen× thirteen× 13	2197
14	14× fourteen× 14	2744
fifteen	xv× fifteen× 15	3375
16	16× xvi× 16	4096
17	17× 17× 17	4913
18	xviii× 18× 18	5832
xix	19× 19× 19	6859
20	20× 20× twenty	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× xxx× 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
twoscore	40× 40× forty	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
fifty	50× 50× 50	125000

How to Find a Perfect Cube?

Every number can be expressed equally the product of the ability of its Prime factors. If the ability of all the Prime number factors is in the multiple of three, and so the number is said to be a perfect cube.

1) xv = 3 × v

15³= xv × 15 × fifteen = three × 5 × 3 × 5 × 3 × v = 3³× 5³

2) eighteen = 2 × three × 3

18³ = 18 × xviii × 18 = 2 × iii × 3 × two × 3 × 3 × 2 × 3 × three = twoⁱⁱⁱ × 3³× 3^three

From the above examples, we can observe that each prime gene of a number appears 3 times in the prime factorization of its cube.

Cube
Cubes From i to fifty
Cube Root i to 30
Squares upto 50
How to Discover Cube Root
Cube Roots of Unity
Perfect Numbers

Solved Examples on Perfect Cubes

Question one: Is the number 600 a perfect cube?

Permit us write down, stating the prime factors of the number 600.

\(\begin{assortment}{l}600 = 2 \times 2\times 2 \times 3 \times v \times 5 = 2^{3}.three.v^{2} \end{array} \)

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

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

\(\begin{array}{fifty} Factors\ of\ 120 = 2 \times 2 \times 2 \times 3 \times five = two^{3}. 3.v\end{array} \)

The factor 2 occurs thrice, three and 5 occurs only in one case. So in order to make it a perfect cube nosotros take to multiply 120 with a foursquare of iii and v.

Therefore, 120 × three × 3 × 5 × five =27000

The number 27000 is the required perfect cube.

Application of Perfect Cubes

A cube is a three-dimensional figure which has all the edges of equal length. The volume of a cube is given by the production of its dimensions. For instance, for a cube of edge length 'a' units, the book of the cube is given by "a × a × a"which is equal to a³cubic unit. Similarly, we tin can summate the perfect cube of various numbers.

Perfect Cube

Analogy: Determine the volume of a cube with an border length of 7 cm.

Solution: The side of the cube is 7 cm.

Volume = side × side × side = vii × vii × vii = 343 cm³.

The numbers such as 1, 8, 27, 64, etc. are known as perfect cubes or cube numbers.

When a cube is cleaved or cut, full volume even so remains the same. Hence, nosotros can observe that to construct a cube of edge length '2a' with cubes of edge length 'a' we need to have viii cubes of edge length a.

This commodity explains perfect cubes and the method of their calculation. To acquire more about other topics download BYJU'S – The Learning App and sentry interactive videos. Also, take free tests to practice for exams.

Frequently Asked Questions on Perfect Cubes

What is a perfect cube?

When a natural number is multiplied 3 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 x 100 = million

What are first 10 perfect cube numbers?

The kickoff ten cube numbers are 1, eight, 27, 64, 125, 216, 343, 512, 729 and grand.

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

27 is the perfect cube. Since 3 ten three x three = 3³ = 27
9 and 400 are the perfect squares. 3 x 3 = nine and 20 10 20 = 400

What is the cube thirty?