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1. Maths Presentation
Finding Cube Root of a number by Prime Factorisation

2. What is Cube?

3. In math, a cube is a number multiplied by itself three times. The cube of
2 is 8 (2 x 2 x 2).
Cube

4. Cube of numbers from 1 - 20

7. What are Perfect Cubes?

8. A perfect cube is a number that is the cube of an integer.
For example, 125 is a perfect cube since 125 = 5 × 5 × 5 =
53. Some other examples of perfect cubes are 1, 8, 27, 64,
125, 216, 343, …
Perfect Cube

9. What are Non-Perfect Cubes?

10. There are many numbers which are not perfect cubes
and we cannot find the cube root of such numbers using
the prime factorisation and estimation method. Let us
find the cube root of 150 here. Clearly, 150 is not a perfect
cube. It will be around 5.31. So the cube root value of non
perfect cubes are in decimals or not integers.
Non-Perfect Cube

11. What is Cube Root?

12. In mathematics, a cube root of a number x is a number y
such that y³ = x. All nonzero real numbers, have exactly
one real cube root and a pair of complex conjugate cube
roots, and all nonzero complex numbers have three
distinct complex cube roots.
Cube Root

13. 3 27
CUBE
CUBE ROOT
3 ✕ 3 ✕ 3

15. What is Prime Factorisation?

16. Prime factorization of any given number is to breakdown
the number into its factors until all of its factors are prime
numbers. This can be achieved by dividing the given
number from smallest prime number and continue it until
all its factors are prime.
Prime Factorisation

17. Finding Cube Root by Prime Factorisation

18. In order of finding cube root by prime factorization we use the following
steps :
Step I : Obtain the given number.
Step II : Resolve it into prime factors.
Step III : Group the factors in 3 in such a way that each number of the
group is same.
Step IV : Take one factor from each group.
Step V : Find the product of the factors obtained in step IV. This product
is the required cube root.
Steps to Find Cube Root by Prime Factorisation

19. Solved Example #1

20. First of all we will factorise 1728 (as shown in the figure).
Now we will write all the prime factors obtained as -
1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
Then we will make groups of three same numbers and write one
common of them as -
1728 = [2 × 2 × 2] × [2 × 2 × 2] × [3 × 3 × 3]
= 2 × 2 × 3
= 12
Therefore, cube root of 1728 is 12.
Find the cube root of 1728.

21. Solved Example #2

22. First of all we will factorise 970299 (as shown in the figure).
Now we will write all the prime factors obtained as -
970299 = 3 × 3 × 3 × 3 × 3 × 3 × 11 × 11 × 11
Then we will make groups of three same numbers and write one
common of them as -
1728 = [3 × 3 × 3] × [3 × 3 × 3] × [11 × 11 × 11]
= 3 × 3 × 11
= 99
Therefore, cube root of 970299 is 99.
Find the cube root of 970299.