 # Cube Root List 1 to 30  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 30 will help students to solve the cube root problem easily, accurately, and with speed.

### How to Find Cube Root of Non-Perfect Cubes?

We cannot find the cube root of numbers which are not perfect cube using the prime factorization and estimation method. Hence, we will use here some other method.

Let us find the cube root of 30 here. Here, 30 is not a perfect cube.

Step 1:

Now we would see 30 lies between 27 ( the cube of 3) and 64 (the cube of 4). So, we will consider the lower number here, i.e. 3.

Step 2:

Divide 30 by square of 3, i.e., 30/9 = 3.33

Step 3:

Now subtract 3 from 3.33 (whichever is greater) and divide it by 3. So,

3.33 - 3  = 0.33 & 0.33/3 = 0.11

Step 4:

At the final step, we have to add the lower number which we got at the first step and the decimal number obtained.

So, 3 + 0.11  = 3.11

Therefore, the cube root of 30 is ∛30 = 3.11

This is not an accurate value but closer to it.

Let us find the cube root of 1 to 30 natural numbers

### Cube Root of 1 to 30

The cube root from 1 to 30 will help students to solve mathematical problems. A list of cubic roots of numbers from 1 to 30 is provided herein 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 30.

 Number Cube Root ( ∛ ) 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

### Solved Examples

Example 1:  Solve ∛4 + ∛7.

Solution:

From the table, we can get the value of ∛4 and ∛7

∛4 = 1.587

∛7 = 1.913

Therefore,

∛4 + ∛7 = 1.587 + 1.913

= 3.5

Example 2: Evaluate the value of 4 ∛9

Solution:

We know,

∛9 = 2.080

Therefore,

4 ∛9 = 4 x 2.080

= 8.32

### Quiz Time

Find the Value of:

1. Evaluate 3∛9 + 7

2. Solve ∛7 - ∛3

1. How to Find the Cube Root of Large Numbers Quickly?

One simple and easy tip for finding Cube Roots of Perfect Cubes of two digits numbers. By this cube root formula, we find the cube root in a fraction of seconds.

These points to be remembered for this cube root formula.

• The given number should be a perfect two-digit cube.

• Remember cubes of 1 to 10 numbers.

• As per the cubes identify as follows as below table.

 13 = 1 If last digit of perfect cube number is 1, the last digit of cube root for that number will be 1 23 = 8 If last digit of perfect cube number =8, last digit of cube root for that number=2 33 = 27 If last digit of perfect cube number =7, last digit of cube root for that number=3 43 = 64 If last digit of perfect cube number =4, last digit of cube root for that number=4 53 = 125 If last digit of perfect cube number =5, last digit of cube root for that number=5 63 = 216 If last digit of perfect cube number is 6, last digit of cube root for that number will be 6 73 = 343 If last digit of perfect cube number =3, last digit of cube root for that number=7 83 =512 If last digit of perfect cube number =2, last digit of cube root for that number=8 93 = 729 If last digit of perfect cube number is 9, last digit of cube root for that number will be 9 103 = 1000 If last digit of perfect cube number is 0, last digit of cube root for that number will be 0

Consider an example to easily understand the cube root formula

Example: Find Cube Root of 13824

Step 1

Identify the last three digits from the right side and make a group of these three digits

i.e., 13 – 824

Step 2

Take the last group which is 824. And then find the last digit of 824 is 4

According to the above table if the last digit of perfect cube number is  4 then the last digit of cube root for that number will be 4

Hence the rightmost digit of the cube root of the given number is 4

Step 3

Take the next group which is 13

The value of 13 lies  between the cube of the numbers 23 and 33

8 < 13 < 27

Take small cube number i.e “ 2 “

Hence the left side digit of the answer is 2

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