 # Cube Root List 1 to 100  View Notes

## What is Cube Root?

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.

### Cube Root of 1 to 30

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.

## Cube Root List 1 to 100

 Number Cube Root (3√) 1 1.000 2 1.260 3 1.442 4 1.587 5 1.710 6 1.817 7 1.913 8 2.000 9 2.080 10 2.154 11 2.224 12 2.289 13 2.351 14 2.410 15 2.466 16 2.520 17 2.571 18 2.621 19 2.668 20 2.714 21 2.759 22 2.802 23 2.844 24 2.884 25 2.924 26 2.962 27 3.000 28 3.037 29 3.072 30 3.107 31 3.141 32 3.175 33 3.208 34 3.240 35 3.271 36 3.302 37 3.332 38 3.362 39 3.391 40 3.420 41 3.448 42 3.476 43 3.503 44 3.530 45 3.557 46 3.583 47 3.609 48 3.634 49 3.659 50 3.684 51 3.708 52 3.733 53 3.756 54 3.780 55 3.803 56 3.826 57 3.849 58 3.871 59 3.893 60 3.915 61 3.936 62 3.958 63 3.979 64 4.000 65 4.021 66 4.041 67 4.062 68 4.082 69 4.102 70 4.121 71 4.141 72 4.160 73 4.179 74 4.198 75 4.217 76 4.236 77 4.254 78 4.273 79 4.291 80 4.309 81 4.327 82 4.344 83 4.362 84 4.380 85 4.397 86 4.414 87 4.431 88 4.448 89 4.465 90 4.481 91 4.498 92 4.514 93 4.531 94 4.547 95 4.563 96 4.579 97 4.595 98 4.610 99 4.626 100 4.642

### Finding the Cube Root of a Perfect Cube

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.

Find ∛343

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

### Solved Examples

Example 1:  Solve ∛4 - ∛2.

Solution: From the table, we can get the value of ∛4  and ∛2

∛4 = 1.587

∛2 = 1.260

Therefore,

∛4  + ∛2 = 1.587 + 1.260

= 0.327

Example 2: Evaluate the value of 6∛4

Solution: We know

∛4 = 1.587

Therefore,

6∛4  = 6 x 1.587

= 9.522

### Quiz Time

Find the value of:

1. Evaluate 3∛9 + 7∛4

2. 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.

(A) 22

(B) 21

(C) 23

(D) 24

Solution

 3 9261 3 3087 3 1029 7 343 7 49 7 7 1

Prime factors of 9261

= (3×3×3)×(7×7×7)

Now, taking one number from each group of three, and evaluating it we get

= 3 x 7

∛9261 = 21

Cube Root List 1 to 30  Cube Root List 1 to 20  How to Find Cube Root?  Cube Root  Cube Root Table  Cube Root of 9261  Cube Root of 216  Cube Root of 64  Cube Root of 1728  Cube Root of 2  