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.
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 |
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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