Cube Root of 2

The cube root of 2, denoted as ³√2, is the value that gives the original number when multiplied by itself thrice. This definition is applicable to all the cube roots of natural numbers. Now, since 2 is not a perfect cube, therefore we cannot find it using the prime factorisation method.

We will try to find the value of ³√2, without using a calculator and using the approximation method.

Also read:

• Cube Root Of Unity
• Square Root And Cube Root
• How to find cube root
• Cube root table

Calculation of Cube Root of 2

As we already know, 2 is not a perfect cube, therefore we cannot use the general methods, to find its cube root. Let us find it by using approximation or we can also say, an estimation method.

Assume, ³√2 = X

So, here X should be equal to a number, which after getting multiplied by itself three times, gives the result as 2.

But if we see, 2 is nearly equal to the cube of 1, i.e. 1³ = 1

So let us just say,

X = p × p × q

Take p =1 and q = 2

X = 1 × 1 × 2 = 2

This is possible only when the average of the three factors (1,1,2) is roughly equal to the cube root of 2.

Hence,

³√2 = (1+1+2)/3 = 4/3 = 1.3

Again let us say p = 1.3 and q = 1.18

So,

1.3×1.3×1.18 = 1.99 ≈ 2

Taking the average of three factors, 1.3,1.3 and 1.18, we get;

³√2 = (1.3+1.3+1.18)/3 = 3.78/3 = 1.26

Hence,

³√2 = 1.26

Therefore, we get the value of the cube root of 2 equal to 1.26, which is approximately equal to its actual value, i.e.,1.2599210.

Cube Root of Non-Perfect Cubes

To find the cube root of perfect cubes is easy, but difficult to find for the non-perfect cubes.

For example, the cube root of 27 is equal to 3.

Since, 27 = 3 x 3 x 3 = 3³

Therefore,

³√27 = ³√(3³) = 3

But for non-perfect cubes we cannot find their cubic roots this easily. Thus, here is a table for the cube roots from 1 to 20 consisting of only non-perfect cubes.

From the table, we can see there are only two numbers eliminated from the table between 1 and 20, which are 1 and 8. Apart from that, all the natural numbers are non-perfect cubes.

Video Lesson on Finding Cube Roots