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Perfect Cube Root

Maths

Perfect Cube Root

Last updated date: 28th Apr 2024

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What is Perfect Cube Root?

A perfect cube is the result of multiplying the same integer three times. Repeating the number 4 times three makes 64 and as a result 64 is a perfect cube. 64 has a cube root of 4. If a number can be decomposed into a product of the same three numbers, it is said to be a perfect cube.

A complete cube is the product of three identical numbers. To see if the number (for example n) is a suitable cube,multiply it by three times and check if the resulting number is the same as 'n' if yes then it is a perfect cube

One, eight, twenty-seven, and sixty-four are examples of perfect cubes. A perfect square is one that can be made by multiplying two numbers together. Both positive and negative numbers can be used to make perfect cubes. Because it is the product of multiplying -4 three times, -64 is a perfect cube.

When we say a number has been cubed, we mean that it has been multiplied three times. The process of cubing a number is reversed by its root. When the number 5 is cubed, for example, we obtain 55 5, which is 125. The cube root of 5 is 125. This is because multiplying the number 5 three times gives the result of 125.It is the same as the square root symbol with an addition of '3' to indicate it is a cube root .The cube root of a number can be stated in exponent form as (number)13.

Cube root table

Cube root table is a table consisting of a list of numbers and their cube roots. Before we write the cube root table, it is very important for all of us to understand what is the perfect cube root chart and cube of a number. The cube of any real number can be defined as that number which is obtained by multiplying a number by itself twice or by raising its power to 3. At the same time, the cube root of any number is that number which when raised to the power 3 gives the answer as the number whose cube root is to be determined.

Perfect Cube Root Chart

Perfect Cube Number	Cube Root of the Number
1	1
8	2
27	3
64	4
125	5
216	6
343	7
512	8
729	9
1000	10
1331	11
1728	12
2197	13
2744	14
3375	15
4096	16
4913	17
5832	18
6859	19
8000	20
9261	21
10648	22
12167	23
13824	24
15625	25

Cube root of a number can also be exponentially represented as the number raised to the power ⅓. If ‘x’ is any real number, then its cube root is represented as (x)⅓ or ∛x. Perfect cubes are the numbers that are obtained when natural numbers are multiplied by itself twice. All the perfect cube numbers have a square root equal to a natural number. The perfect cube root chart of the first 25 perfect cube numbers is represented in the table below.

While it is very important to know the cube roots of the numbers, it is also very important to know the table of cubes from 1 to 50 (i.e. first 50 natural numbers) in order to make our Mathematical computations easy and efficient without a calculator. The table of cubes from 1 to 50 is given below for the reference of students and facilitators.

Table of Cubes from 1 to 50

Natural Number	Cube of the Number
1	1
2	8
3	27
4	64
5	125
6	216
7	343
8	512
9	729
10	1000
11	1331
12	1728
13	2197
14	2744
15	3375
16	4096
17	4913
18	5832
19	6859
20	8000
21	9261
22	10648
23	12167
24	13824
25	15625
26	17576
27	19683
28	21952
29	24389
30	27000
31	29791
32	32768
33	35937
34	39304
35	42875
36	46656
37	50653
38	54872
39	59319
40	64000
41	68921
42	74088
43	79507
44	85184
45	91125
46	97336
47	103823
48	110592
49	117649
50	125000

Any student or a facilitator who is keen about Mathematics will find his or her own ways to memorize the cube root list 1 to 100. Though it may seem a little difficult at the initial days, the task of remembering the cube root list 1 to 100 becomes more and more easy through continuous practice and periodic revision.

Cube Root List 1 to 100

Number	Cube Root	Number	Cube Root	Number	Cube Root	Number	Cube Root
1	1.000	26	2.962	51	3.708	76	4.236
2	1.260	27	3.000	52	3.733	77	4.254
3	1.442	28	3.037	53	3.756	78	4.273
4	1.587	29	3.072	54	3.780	79	4.291
5	1.710	30	3.107	55	3.803	80	4.309
6	1.817	31	3.141	56	3.826	81	4.327
7	1.913	32	3.175	57	3.849	82	4.344
8	2.000	33	3.208	58	3.871	83	4.362
9	2.080	34	3.240	59	3.893	84	4.380
10	2.154	35	3.271	60	3.915	85	4.397
11	2.224	36	3.302	61	3.936	86	4.414
12	2.289	37	3.332	62	3.958	87	4.431
13	2.351	38	3.362	63	3.979	88	4.448
14	2.410	39	3.391	64	4.000	89	4.465
15	2.466	40	3.420	65	4.021	90	4.481
16	2.520	41	3.448	66	4.041	91	4.498
17	2.571	42	3.476	67	4.062	92	4.514
18	2.621	43	3.503	68	4.082	93	4.531
19	2.668	44	3.530	69	4.102	94	4.547
20	2.714	45	3.557	70	4.121	95	4.563
21	2.759	46	3.583	71	4.141	96	4.579
22	2.802	47	3.609	72	4.160	97	4.595
23	2.844	48	3.634	73	4.179	98	4.610
24	2.884	49	3.659	74	4.198	99	4.626
25	2.924	50	3.684	75	4.217	100	4.642

Steps To Find Out Perfect Cube Root

Following the steps below, you can check if a number is a perfect cube:

Step 1: Starting with the smallest prime number, prime factorise the given number (2).

Step 2: Once the prime factorization is complete, group together all three identical factors.

Step 3: Repeat Step 3 for all sets of the same three factors in the group. The provided number is not a perfect cube if any factors are left over that do not fit into a group of three identical factors. The provided integer is otherwise a perfect cube.

Fun Fact About Cube Root

Cube and cube roots are inverse mathematical operations.
The Cube of a cube root of a number or the cube root of a cube of a number is the number itself.

There is a method for determining whether or not greater integers are perfect cubes. To check, find the sum of the number's digits repeatedly and see if it's either 0, 1, 8, or 9. If it's any of these, it could be a perfect cube, although that isn't always the case.

Perfect Cube Formula

The perfect cube formula is used to determine whether or not a number is a perfect cube. Let's say we have a number, x, that equals yyy. Every composite number can be written as the product of the powers of its prime elements, according to the fundamental theorem of arithmetic. The number is considered to be a perfect cube if the power of all prime factors is a multiple of three.

From 1 to 50, this is a list of perfect cubes.

In the table below, the perfect cubes of integers 1 to 50 are presented. Every integer is multiplied three times by itself to get the ideal cubes.

1	1 × 1 × 1	1
2	2 × 2 × 2	8
3	3 × 3 × 3	27
4	4 × 4 × 4	64
5	5 × 5 × 5	125
6	6 × 6 × 6	216
7	7 × 7 × 7	343
8	8 × 8 × 8	512
9	9 × 9 × 9	729
10	10 × 10 × 10	1000
11	11 × 11 × 11	1331
12	12 × 12 × 12	1728
13	13 × 13 × 13	2197
14	14 × 14 × 14	2744
15	15 × 15 × 15	3375
16	16 × 16 × 16	4096
17	17 × 17 × 17	4913
18	18 × 18 × 18	5832
19	19 × 19 × 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	30 × 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	40 × 40 × 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

Conclusion

This is how we can easily calculate perfect cube roots of different numbers. Focus on the concept of perfect cube roots and understand how they are determined. Follow the examples given in the tables and charts here to develop your conceptual foundation.

FAQs on Perfect Cube Root

1. Where do we use Cubes and Cube Roots?

Cubes and cube roots are used in several Mathematical and Physical computations. It is quite often used to derive the solutions of cubic equations. To be more specific, the knowledge of cube roots can be used to determine the dimensions of three dimensional objects with specific value. Cubes and cube roots are also used in day to day calculations of Mathematics while learning the concepts such as exponents.

2. Why is it Important to know the Short Tricks of Finding Cubes and Cube Roots?

Cubes and cube roots are the most favorite topics of the paper setters who frame question papers for competitive examinations. It is highly difficult to crack these exams without the knowledge of short tricks to find cubes and cube roots because most of the questions in these exams are time bound and restricts the use of calculators. So, the continuous practice of a few short tricks and tips to remember the cubes and cube roots of at least few numbers may help a lot.