Find the cube root of -42875
Answers
Cube root of a number can be found by a very simple method which is the prime factorization method. Cube root is denoted by ‘∛ ‘ symbol. Example: ∛8 = ∛(2 × 2 × 2) = 2. Since, 8 is a perfect cube number, it is easy to find the cube root of a number.
Finding the cubic root of non-perfect cube number is a little complex process but can be mastered easily. To find the cube root of any number, we need to find a number which when multiplied three times by itself gives the original number.
Let us learn here finding cube root using prime factorisation method and solved examples. Also, find the cubes and cube roots of 1 to 15 numbers here in the table given.
Table 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 satisfy the equation given below:
b3 = a
This can be represented as:
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 us see some examples here now.
To find the cube root of a number 27, we want a number which when multiplied thrice with itself shall give 27. We can write,
27 = 3 × 3× 3 = 33
Taking cubic root on both the sides;
or ∛27 = ∛33
Therefore, the cube-root of 27 is 3.
Please note that we will only consider the positive values cube roots of the natural numbers.
Cube Root of 2
Let us consider another example of number 2. Since 2 is not a perfect cube number. It is not easy to find 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 approximate value of the ∛2 is 1.260.
We can estimate the ∛2 by using the trick here.
Since, 2 = 1 x 1 x 2
Cube root of 2 is approximately equal to (1 + 1+2)/3 = 4/3 = 1.333..