Important Formulas: Cube & Cube roots | Mathematics (Maths) Class 8 PDF Download

Cube Number

Numbers obtained when a number is multiplied by itself three times are known as cube numbers
Example:
1=1³
8=2³
27=3³

Some Important point to Note

• All cube numbers can end with any digit unlike square number when end with 0, 1, 4, 5, 6 or 9 at unit’s place 
• if a number has 1 in the unit’s place, then it’s cube ends in 1.
• Even number cubes are even while odd number cubes are Odd
• There are only ten perfect cubes from 1 to 1000
• There are only four perfect cubes from 1 to 100

Prime Factorization of Cubes

Cube Root

Cube root of a number is the number whose cube is given number
So we know that 27=3³
Cube root of 27
27 = 3
Cube root is denoted by expression

How to Find cube root

1. Finding cube root through prime factorization: This method, we find the prime factorization of the number. We will get same prime number occurring in triplet for perfect cube number. Cube root will be given by multiplication of prime factor occurring in pair
Consider 74088 = 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7 = 2³ × 3³ × 7³ 
= 2 x 3 x 7 = 42

2. Finding cube root by estimation method: This can be well explained with the example The given number is 17576.

• Step 1: Form groups of three starting from the rightmost digit of 17576. 17 576. In this case one group i.e., 576 has three digits whereas 17 has only two digits.
• Step 2: Take 576. The digit 6 is at its one’s place. We take the one’s place of the required cube root as 6.
• Step 3: Take the other group, i.e., 17. Cube of 2 is 8 and cube of 3 is 27. 17 lies between 8 and 27. The smaller number among 2 and 3 is 2. The one’s place of 2 is 2 itself. Take 2 as ten’s place of the cube root of 17576. 
• Thus,