Cube Root of 3

What is a Cube of 3?

When we say the cubed root of 3, then it would mean 27. This is calculated as (3x3x3). When a number is cubed, it implies that it is multiplied itself by 3 times. So 3 cubes is 27. For example, If you have 7 to the power of 3 (or cubed, as 3 implies cubed in math) then to solve, I would say 7 multiplied by itself 3 times. 7x7x7, this comes out to be 343(7x7 is 49, and 49x7 is 343).


How to Determine the Cube Root of 3?

Before we proceed to learn finding the cube root of number 3, we have to first acquaint ourselves in knowing the cubes of the numbers stated below.


Number (x)

Cube of Number (x³)

Output (Perfect Cubes)

1

1×1×1

1

2

2×2×2

8

3

3×3×3

27

4

4×4×4

64

5

5×5×5

125

6

6×6×6

216

7

7×7×7

343

8

8×8×8

512

9

9×9×9

729

10

10×10×10

1000

11

11×11×11

1331

12

12×12×12

1728

13

13×13×13

2197

14

14×14×14

2744

15

15×15×15

3375


Cube Root Lists

Below is a tabular form for the cube root of numbers from 1 to 15.


Number

Cube Root \[\sqrt[3]{n}\]

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


Cube Root of 3 Explained

The cube root of any number n will be a number x, such as x³ = n. Thus, in order to identify the cube root of three, we are required to determine a number, which when multiplied three times with the number itself, provides the number 3, such as x³ = 3 or x = \[\sqrt[3]{3}\]. Hence, we will here require finding the value of x.


The value of the cube root of 3, \[\sqrt[3]{3}\], is equivalent to 1.44224957031. Seeing that 3 do not make a perfect cube, hence it is a bit difficult to determine its cube root. However, for perfect cubes like 8, 27, 64, 125 729 etc., the cube root of such numbers are whole numbers, since, 3³ = 3×3×3 = 27 and 5³ = 5×5×5 = 125. Therefore, the cube root of 125 is 5 and of 27 is 3.


Thus, for 3 in cubed, then you would multiply it 3 times. 3³ = 3x3x3; 3x3 is 9, and 9x3 is 27. Hence, the 3 cubed is 27.


Cube Root Symbol

The symbol of cube root is as ‘\[\sqrt[3]{}\]’

Cube root can also be determined by the approximation method.


Step-By-Step Process to Find Cube Root Easily

Now, let us find out the value of \[\sqrt[3]{3}\], in a detailed step by step manner.

Let us suppose that the cube root of 3 is equivalent to x.

Then, x = \[\sqrt[3]{3}\]

As we are already aware,

1³ = 1 and 2³ = 8

Thus, x lies in between 1 and 8. But, it lies near to the number 1 than 8, if we observe in a number line. Therefore, we can presuppose a value; say 1.4, which could be an approximation to the cube root of 3.

Now, in order to identify the value of \[\sqrt[3]{3}\], we are required to divide 3 by an approx value.

Dividing 3 by 1.4, we get

3/1.4 = 2.1428

Again, we need to divide this value by 1.4.

On dividing, we get,

2.1428/1.4 = 1.53

Now, taking the average of 1.4, 1.4 and 1.53 in order to obtain the value of \[\sqrt[3]{3}\].

(1.4+1.4+1.53)/3 = 1.44

Thus, the actual value of \[\sqrt[3]{3}\] = 1.442249.

Therefore, 1.44 is approximately equivalent to 1.442249.

FAQs (Frequently Asked Questions)

Q1. What is Meant by the Cube Root?

Answer: Let's suppose we want to find the cube root of a number, n. The cube root, x, is such a number that, if raised to the third power, will provide ‘n’ as an outcome. If we formulate this mathematically,

∛n = x ⟺ x³ = n

where ⟺ is a mathematical sign that typically indicates if and only if.

It is also feasible to mathematically write the cube root in a different way, which is often much more convenient. It is due to the fact that a cube root is a unique case of exponent and can be written as:

∛ (n) = n1/3

Q2. How Do We Find the Cube Root of Six?

Answer: Let undertake a geometric example that may help you understand finding the cube root easily. The best example we can consider would be that of the cube. Well, simply understand it this way that the cube root of a cubes volume is its edge length. So, for instance, if a cube has a volume of 216 cm³, then the length of its edges are equivalent to the cube root of 216 cm³, which is 6 cm. Understood? Find it Easy?


You should note that in most cases the cube root is not a rational number. These numbers can be displayed as a quotient of two natural numbers, i.e. a fraction. Fractions can cause some complexities, particularly when it comes to adding them up. If you are having difficulty with finding a common denominator of two fractions, check out the LCM calculator available at Vedantu which estimates the LCM as well as HCF (highest common factor) of two given numbers.