Cube and Cube Roots | Perfect Cube, How to Find the Cube Root, Properties

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Cube and Cube Root of numbers can be found easily using the simplest and quickest methods. Check the complete details of the How to Find the Cube and Cube Root of a Number? We have covered everything like the definition of cube and Cubes Relation with Cube Numbers, Perfect Cube, etc. For better understanding, we even jotted the solved examples explained in detail.

Cube

The cube of a number is calculated by multiplying a number itself by 3 times. If you consider a number n, then the cube of a number n is n. Here, n is the natural number.

Example:

1, 8, 27 are the cube number of the numbers 1, 2, and 3 respectively.

Cube of 9 = 9 × 9 × 9 = 729
Cube of 8 = 8 × 8 × 8 = 512
Cube of 6 = 6 × 6 × 6 = 216

Cubes Relation with Cube Numbers

In mathematics, a cube is defined as a solid figure where all edges are of the same sizes and each edge is perpendicular to other edges.

Example:

If you take cubes of 4 units, then you can form a bigger cube of 64 units. Or else, if you take cubes of 3 units, then you can form a bigger cube of 27 units.

Perfect Cube Cube Numbers

The product of the three same numbers will give you a cube of a number (perfect cube).

Example:

The cube of a number 2 is 2 × 2 × 2 = 8.
8 is a perfect cube.

Properties of Cube Numbers

1. The cube of an even number is always an even number.

Example:
(i) Find the cube of a number 2?
2 × 2 × 2 = 8
8 is an even number.
(ii) Find the cube of a number 4?
4 × 4 × 4 = 64
64 is an even number.
(iii) Find the cube of a number 6?
6 × 6 × 6 = 216

2. The cube of an odd number is always an odd number.

Example:
(i) Find the cube of a number 3?
3 × 3 × 3 = 27
27 is an odd number.
(ii) Find the cube of a number 5?
5 × 5 × 5 = 125
125 is an odd number.
(ii) Find the cube of a number 7?
7 × 7 × 7 = 343
343 is an odd number.

Units Digits in Cube Numbers

If a number is even or odd, its cube is even or odd respective to the given number. The cube of a unit’s digit always shows the below results.

(i) Cube of 1 = 1 × 1 × 1 = 1;
The Units Digits of Cube of 1 is 1.
(ii) Cube of 2 = 2 × 2 × 2 = 8
The Units Digits of Cube of 2 is 8.
(iii) Cube of 3 = 3 × 3 × 3 = 27
The Units Digits of Cube of 3 is 7.
(iv) Cube of 4 = 4 × 4 × 4 = 64
The Units Digits of Cube of 4 is 4.
(v) Cube of 5 = 5 × 5 × 5 = 125
The Units Digits of Cube of 5 is 5.
(vi) Cube of 6 = 6 × 6 × 6 = 216
The Units Digits of Cube of 6 is 6.
(vii) Cube of 7 = 7 × 7 × 7 = 343
The Units Digits of Cube of 7 is 3.
(viii) Cube of 8 = 8 × 8 × 8 = 512
The Units Digits of Cube of 8 is 2.
(ix) Cube of 9 = 9 × 9 × 9 = 729
The Units Digits of Cube of 9 is 9.

Cube roots

Cube Root of a Number is the inverse of finding the cube of a number. If the cube of a number 3 is 27, then the cube root of 27 is 3.

How to Find the Cube Root of a Number by Prime Factorisation Method?

The Prime Factorisation of any Number Cube Root can be calculated by grouping the triplets of the same numbers. Multiply the numbers by taking each one from each triplet to provide you the Cube Root of a Number.

Example:
Cube Root of 216 = 2 × 2 × 2 × 3 × 3 × 3 = 2 × 3 = 6
6 is the cube root of 216.

FAQs on Cube and Cube Roots

1. Find the cube of 3.4?
The cube of a number can be calculated by multiplying it three times.
Cube of 3.4 = 3.4 x 3.4 x 3.4 = 39.304

2. Is 288 a perfect cube? If not, find the smallest natural number by which 288 should be multiplied so that the product is a perfect cube.
The prime factorization of 288 is
288 = 2 x 2 x 2 x 6 x 6
Since we can see number 6 cannot be paired in a group of three. Therefore, 288 is not a perfect cube.
To make it a perfect cube, we have to multiply the 6 by the original number.
Thus, 2 x 2 x 2 x 6 x 6 x 6 = 1728, which is a perfect cube.
Hence, the smallest natural number which should be multiplied to 288 to make a perfect cube is 6.

3: Find the smallest number by which 256 must be divided to obtain a perfect cube.
The prime factorization of 256 is
256 = 2×2×2×2×2×2×4
Now, if we group the factors in triplets of equal factors,
256 = (2×2×2)×(2×2×2)×4
Here, 4 cannot be grouped into triples of equal factors.
Therefore, we will divide 256 by 4 to get a perfect cube.

4. Michael makes a cuboid of plasticine of sides 3 cm, 2 cm, 3 cm. How many such cuboids will he need to form a cube?
Given that the sides of the cube are 3 cm, 2 cm, and 3 cm.
Therefore, volume of cube = 3×2×3 = 18
The prime factorization of 18 = 3×2×3
Here, 2, 3, and 3 cannot be grouped into triplets of equal factors.
Therefore, we will multiply 18 by 2×2×3 = 12 to get a perfect square.
Hence, 12 cuboids are needed.

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