Cube Root of 2

Cube root of 2 is 1.259921… In the radical form, cube root of two is represented as ∛2, and in the exponent form, as (2)^1/3. Cube root of any number is defined as a number which when multiplied by itself twice results in the original number. So cube root of 2 is a number which when multiplied by itself twice results in 2.

Cube Root of 2

In this article, we will learn to find the cube root of 2 with various methods and others in detail.

What is Cube Root of 2?

The number that results in the product of two when multiplied by itself three times is known as the cube root of 2. Whereas, the given number 2 is a prime number. Therefore, 2’s cube root is equal to ∛2 in 6 decimal points 1.2599.

³√2 = 1.2599…

Cube Root Definition

Cube root of a number is a value that gives the original number when multiplied by itself two times. ∛x or (x)^1/3 are symbols for the cube root.

For example; 2 is the cube root of 8 as 2 × 2 × 2 = 8.

Cube Root of 2 Calculator

How to Find Cube Root of 2?

2 is not a perfect cube and hence its cube root can not be found using general methods. Now we will try to find the cube root of 2 using the approximation method.

Assume, ³√2 = X

We know that,

1³ = 1

Let say,

X = p × p × q

Take p =1 and q = 2

X = 1 × 1 × 2 = 2

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

Hence,

³√2 = (1 + 1 + 2)/3 = 4/3 = 1.3

Thus, we get the value of the cube root of 2 equal to 1.3, which is approximately equal to its actual value, i.e.,1.2599210.

Using Halley’s Method

Halley’s Method is a root-finding procedure that is also referred to as the tangent hyperbolas method or Halley’s rational formula. The following formula can also be used to get the cube root of any given number:

∛a ≈ x × (x³ + 2a) / (2x³ + a)

• a = Number whose cube root is being computed
• x = Integer estimate for cube root

Here a = 2

Let’s x = 1

Since 1³ = 1 and 1 is the nearest perfect cube that is less than 2

∛2 = 1 (1³ + 2 × 2)/(2 × 1³ + 2)) = 1.25

Therefore, the cube root of 2 approximate value is 1.25

Is Cube Root of 2 a Rational or Irrational Number?

Cube root of 2 is an irrational number because ∛2  cannot be expressed in the form of p/q where q ≠ 0. Also, ∛2 has non-terminating decimal expansions which are signs for any number to be an irrational number.

Cube Root of Non-Perfect Cubes

Non perfect cubes are number whose cube root is not an integer. A table added below shows the cube root of non-perfect cubes.

Number	Approximate Cube Root (3√)
2	1.260
3	1.442
4	1.587
5	1.710
6	1.817
7	1.913
9	2.080
10	2.154

Examples on Cube Root of 2

Example 1: Evaluate the value of ∛2 × ∛-2.

Solution

We know, ∛2 = 1.260

Also, ∛-2 = -1.260

Hence, ∛2 × ∛-2 = 1.260 × -1.260 = -1.5876

Example 2: Compute x on x³ = 2.

Solution:

Given x³ = 2

⇒ x = ∛2 = 1.260

Example 3: Find cube root of 64.

Solution:

Factors of 64 are = 2 × 2 × 2 × 2 × 2 × 2

(64)^1/3 = (2 × 2 × 2)^1/3 × (2 × 2 × 2)^1/3

(64)^1/3 = 2 × 2

(64)^1/3 = 4

So, cube root of 64 is 4

Cube Root of 2: FAQs

What is value of cube root of 2?

Approximate value of the cube root of 2 is 1.25992

What is cube of cube root of 2?

Cube of the cube root of 2 is the number 2 itself

Why is value of cube Root of 2 Irrational?

Cube root of 2 is a non-terminating and non-recurring decimal and hence, ∛2 is an irrational number

What is Cube of 2?

Cube of 2 is 8

What is the value of vube root of negative 2?

Cube root of -2 in approximate value is -1.2599