The cube root of a number a is that number which when multiplied by itself three times gives the number ‘a’ itself. The cube root is the inverse operation of cubing a number. The cube root symbols is ∛, it is the “radical” symbol (used for square roots) with a little three to mean cube root.
If n is a perfect cube for any integer m i.e., n = m³, then m is called the cube root of n and it is denoted by m = ∛n.
Cube root list 1 to 100 will help students to solve the cube root problem easily, accurately and with speed.
The cube root from 1 to 100 will help students to solve mathematical problems. List of cubic roots of numbers from 1 to 100 is provided here in a tabular format. The cube root has many applications in Maths, especially in geometry where we find the volume of different solid shapes, measured in cubic units. It will help us to find the dimensions of solids. For example, a cube has volume ‘x’ cubic meter, then we can find the side-length of the cube by evaluating the cube root of its volume, i.e., side = ∛x . Let us see the values of cubic roots of numbers from 1 to 100.
Recall that a perfect cube is the number that is the result of multiplying a number with itself 3 times.
We can think of cube roots in the same context that we view square roots. When we take the square root of a perfect square, we are searching for the number, that when multiplied by itself two times, results in the perfect square. Similarly, when we are finding the cube root of the perfect cube, we are searching for the number that when multiplied by itself three times, results in the perfect cube.
Let's solve an example.
Solution: To find this, we first need to break 343 into its prime factorization. To do so, we need to find the first pair of factors that include a prime number. For 343, this first pair will be 7 and 49. 7 cannot be broken down any further, but 49 can be broken into 7and 7. Therefore, we can say that ∛343= ∛7 x 7 x 7, so we can say that the cube root of 343 is 7, where 7 x 7 x 7 = 343
Example 1: Solve ∛4 - ∛2.
Solution: From the table, we can get the value of ∛4 and ∛2
∛4 = 1.587
∛2 = 1.260
∛4 + ∛2 = 1.587 + 1.260
Example 2: Evaluate the value of 6∛4
Solution: We know
∛4 = 1.587
6∛4 = 6 x 1.587
Find the value of:
Evaluate 3∛9 + 7∛4
Solve ∛9 - ∛3
1. What is Cube and Cube Root ?
Definition of Cube
If a number is multiple three times with itself, then the result of this multiplication is called the cube of that number. Example: cube of 6 = 6 × 6 × 6 = 216.
Definition of Cube Root
The cube root is that number which on cubing itself gives the given number. The cube root is denoted by the symbol ‘ ∛ ’. Example, ∛8 =∛2 × 2 × 2 = 2
2. How to calculate Cube Root of a number by Prime Factorisation Method?
Prime Factorisation Method
This method has the following steps
Step 1: Find the product of prime factors of the given number.
Step 2: Keep these factors in a group of three.
Step 3: Take the product of these prime factors picking one out of every group ( group of three) of the same primes. The product of these numbers gives us the cube root of a given number.
Ex. Find the cube root of 9261.
Prime factors of 9261
Now, taking one number from each group of three, and evaluating it we get
= 3 x 7
∛9261 = 21