cube root kaise nikal te hai
Answers
Step-by-step explanation:
2744= 2 × 2× 2 × 7 ×7 × 7= (2 × 7 )3
Therefore, the cube root of 2744 = ∛2744 = 2 × 7 = 14
Finding Cube Root Using Division Method
For finding the cube root using the division method is similar to using the long division method or manual square method. Make a pair of 3 digit number from the back to front. Next step is to find the number whose cube root is less than or equal to the given number. Now, subtract the obtained number from the given number and write down in the second number. After this step, it is necessary to find the multiplication factor for the further process in the long division method, which comes by multiplying the first number obtained. Similarly continue the above process, to find the cube root of a number. This long division process is used when the given number is not a perfect cube number. Finding the cube root of a number using this process takes a long time.
Cube Root of 64
Since 64 is a perfect cube of 4, therefore, it is easy to find its cube-root by prime factorisation method.
64 = 2 x 2 x 2 x 2 x 2 x 2
∛64 = ∛(2 x 2 x 2 x 2 x 2 x 2)
= 2 x 2
= 4
Cube Root of 216
Since, 216 is perfect cube of 6, hence we can find the cube root of 216 by factorisation.
216 = 2 x 2 x 2 x 3 x 3 x 3
∛216 = ∛(2 x 2 x 2 x 3 x 3 x 3)
∛216 = 2 x 3
∛216 = 6
Cube Root of 343
Let us find the cube root of 343 with the help of the prime factorisation method.
Dividing 343 by smallest prime factor, till we get the remainder as 1. Follow the below steps;

Cube root of 343
Therefore, 343 = 7 × 7 × 7
And, ∛343 = 7
Cube Root of 512
To find the cube root of 512 we have to factorise it first.
The prime factorisation of 512 can be written as:
512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
Taking the cube roots both the sides, we get;
∛512 = ∛(2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2)
∛512 = 2 x 2 x 2
∛512 = 8
Cube Root of 729
Now, let’s find the cubic root of 729.

Cube root of 729
729 = 3 × 3 × 3 × 3 × 3 × 3 = 9 × 9 × 9
Therefore, the cube root of 729 i.e. ∛729 = 9
Cube Root Questions
Question 1: Solve: ∛24389
Solution:
Prime factors = 29×29×29 = 293
Therefore, ∛24389= 29.
Question 2: Find ∛46656 by the method of prime factorization.
Solution:
Let us first find the prime factors:

Cube Root of Numbers
∛46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 = 23 × 23 × 33 × 33 = (2 × 2 × 3 × 3)3
Therefore, ∛46656= 36.

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Frequently Asked Questions
What is the cube root of a number?
The cube root of a number is defined as the number which results in the original number when it is cubed. For example, for 8, the cube root will be 2 as 2×2×2 = 8.
What is the easiest method to find the cube root of a number?
The cube root of perfect cubes can be easily found out by using prime factorisation method as explained in this lesson.
What is a perfect cube?
A perfect cube is defined as any number which is the cube of an integer.
How to know if a number is a perfect cube?
To check whether a number is a perfect cube, factorise the number first. If the factors of the number can be equally grouped in triples, the number is a cube root