how do you find the cube root of a number
Cube root of a number can be found past a very simple method which is the prime factorization method. Cube root is denoted by '∛ ' symbol. Example: ∛8 = ∛(ii × 2 × 2) = two. Since, viii is a perfect cube number, information technology is easy to find the cube root of a number.
Finding the cubic root of not-perfect cube number is a footling circuitous process only tin can be mastered easily. To find the cube root of any number, we demand to observe a number which when multiplied three times by itself gives the original number.
Let u.s.a. larn here finding cube root using prime factorisation method and solved examples. As well, notice the cubes and cube roots of one to 15 numbers here in the tabular array given.
Tabular array of contents:
- Definition
- Finding Cube Root
- Cube root of 2
- Cube root of 4
- Cube Root Lists
- Cube root by Prime Factorisation
- Cube root of 64
- Cube root of 216
- Cube root of 343
- Cube root of 512
- Cube root of 729
- Example Questions
- Video Lesson
- FAQs
Definition
The cube root of any number say 'a', is the number 'b', which satisfies the equation given beneath:
b3= a
This can be represented equally:
a = ∛b
How to Find Cube Root of a Number
Cube root is the inverse process of calculating the cube of a number. It is denoted by the symbol '∛'. Let the states see some examples here now.
To find the cube root of a number 27, we desire a number which when multiplied thrice with itself shall give 27. We can write,
27 = 3 × 3× 3 = three3
Taking cubic root on both the sides;
or ∛27 = ∛iii3
Therefore, the cube-root of 27 is three.
Please notation that nosotros volition only consider the positive values cube roots of the natural numbers.
Cube Root of 2
Let us consider another case of number 2. Since 2 is not a perfect cube number. It is not easy to notice the cube root of 2. With the help of the long division method, it is possible to find the cube roots for non-perfect cube numbers. The estimate value of the ∛2 is one.260.
Nosotros can estimate the ∛2 by using the trick hither.
Since, 2 = 1 x 1 x 2
Cube root of two is approximately equal to (1 + 1+ii)/3 = 4/3 = i.333..
Cube root of 4
Over again 4 is a number, which is non a perfect cube. If we factorise it, we get:
4 = two x 2 10 one
Hence, nosotros tin run into, we cannot discover the cube root by simple factorisation hither.
Again, if we use the shortcut method, we go:
∛4 is equal to (ii+ii+i)/3 = 1.67
The bodily value of ∛4 is i.587, which is approximately equal to 1.67.
Cubes and Cube Roots List of 1 to 15
| Number | Cube(a3) | Cube root ∛a |
|---|---|---|
| 1 | ane | ane.000 |
| 2 | 8 | 1.260 |
| 3 | 27 | i.442 |
| iv | 64 | 1.587 |
| 5 | 125 | 1.710 |
| 6 | 216 | ane.817 |
| seven | 343 | 1.913 |
| 8 | 512 | 2.000 |
| ix | 729 | 2.080 |
| 10 | 1000 | ii.154 |
| 11 | 1331 | 2.224 |
| 12 | 1728 | two.289 |
| 13 | 2197 | 2.351 |
| 14 | 2744 | two.410 |
| 15 | 3375 | ii.466 |
Also, read:
- Cube Root Of Unity
- Cube Root Formula
- Square Root And Cube Root
- Important Questions Class 8 Maths Chapter 7 Cubes Roots
Cube Root By Prime Factorisation Method
We can discover the cube-root of a number by the method of prime number factorisation. Consider the following example for a articulate understanding:
2744= ii × 2× 2 × vii ×7 × vii= (2 × 7 )iii
Therefore, the cube root of 2744 = ∛2744 = 2 × vii = fourteen
Finding Cube Root Using Sectionalisation Method
For finding the cube root using the division method is similar to using the long partitioning method or manual square method. Make a pair of 3 digit numbers from the back to forepart. Side by side footstep is to notice 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 downwardly in the second number. Afterward this footstep, it is necessary to notice the multiplication factor for the farther process in the long division method, which comes past multiplying the first number obtained. Similarly continue the above process, to observe the cube root of a number. This long segmentation procedure is used when the given number is not a perfect cube number. Finding the cube root of a number using this procedure takes a long time.
Cube Root of 64
Since 64 is a perfect cube of iv, therefore, it is easy to find its cube-root by the prime factorisation method.
64 = 2 x 2 ten ii x 2 10 two x 2
∛64 = ∛(2 10 ii 10 2 x 2 x 2 10 2)
= ii x 2
= 4
Cube Root of 216
Since, 216 is perfect cube of 6, hence nosotros can find the cube root of 216 past factorisation.
216 = 2 x two x two x 3 x 3 x three
∛216 = ∛(2 x ii 10 2 10 iii x 3 ten 3)
∛216 = 2 x 3
∛216 = 6
Cube Root of 343
Allow us discover the cube root of 343 with the help of the the prime factorisation method.
Dividing 343 by smallest prime factor, till we get the remainder every bit 1. Follow the below steps;
Cube root of 343
Therefore, 343 = 7 × 7 × 7
And, ∛343 = vii
Cube Root of 512
To detect the cube root of 512 nosotros accept to factorise information technology get-go.
The prime number factorisation of 512 can exist written as:
512 = 2 x two x 2 x 2 x 2 x 2 10 two x 2 x 2
Taking the cube roots both the sides, nosotros get;
∛512 = ∛(2 10 2 x 2 x 2 ten 2 x 2 x 2 10 ii x 2)
∛512 = 2 10 2 ten 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 × ix
Therefore, the cube root of 729 i.e. ∛729 = ix
Cube Root Questions
Question ane: Solve: ∛24389
Solution:
Prime factors = 29×29×29 = 293
Therefore, ∛24389= 29.
Question ii: Discover ∛46656 by the method of prime number factorization.
Solution:
Allow u.s. showtime observe the prime number factors:
Cube Root of Numbers
∛46656 = 2 × 2 × 2 × 2 × ii × two × 3 × 3 × 3 × three × iii × 3 = 23 × 2three × 33 × 33 = (two × two × iii × 3)iii
Therefore, ∛46656= 36.
Video Lesson
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 ii equally two×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 past using prime number factorisation method as explained in this lesson.
What is a perfect cube?
A perfect cube is defined every bit whatever 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 commencement. If the factors of the number can be equally grouped in triples, the number is a perfect cube.
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