# Cube Root of 4

## Trigonometry # Cube Root of 4

The cube root of 4 is a value which on getting multiplied by itself, three times, results in the original number. It is expressed in the form of ‘∛4’. The meaning of cube root is basically the root of a number which is generated by taking the cube of another number. Hence, if the value of ∛4 = x, then x3 = 4 and we need to find here the value of x. In this article, we are going to learn how to find cube root of 4 with complete explanation.

 Cube root of 4, ∛4 = 1.5874

## How to Find the Value of Cube Root of 4?

Since 4 is not a perfect cube, we cannot use here prime factorisation method or estimation method to find the cubic root of 4. Therefore, we are going to use another method here which is called Hallely’s method. Here are the following steps to find the cube root of 4 using Halley’s Method.

Halley’s method formula is: ∛a ≈ x ((x3 + 2a)/(2x3 + a))

Here, “a” is the number whose cube root is being calculated.

“x” is the integer guess of a number

Now, we want to find the cube root of 4. Hence, a = 4.

Let us assume a = 1 since 1 is the nearest perfect cube which is less than 4.

(i.e) 13 = 1.

Hence, x = 1.

Now, substitute the values in Halley’s formula, we get

∛4 = 1 (13 + 2 × 4)/(2 × 13 + 4))

∛4 = 1.5.

Hence, the cube root of 4 is approximately equal to 1.5.

Also, check:

### Cube Root of 4 Examples

Example 1:

Simplify the expression 4 + ∛4.

Solution:

Given: 4 + ∛4.

We know that the value of cube root of 4, ∛4 is approximately equal to 1.5874.

Now, substitute the value in the given expression, we get,

4 + ∛4 = 4+1.5874.

4 + ∛4 = 5.5874.

Hence, 4 + ∛4 = 5.5874.

Example 2:

Find the value of x for the equation: x+2∛4 = 10.

Solution:

Given expression: x+2∛4 = 10

We know that, ∛4 = 1.5874.

Now, substitute the cube root of 4 value in the given equation, we get

x+2∛4 = 10

x+2(1.5874) = 10

x+ 3.1748 = 10

x = 10-3.1748

x = 6.8252.

Hence, the value of x is 6.8252.

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## Frequently Asked Questions on Cube Root of 4

### What is the value of cube root of 4?

The value of cube root of 4 is approximately equal to 1.5874.

### Is the value of cube root of 4 a rational number?

No, the value of the cube root of 4 is not a rational number. The value of cube root of 4 is an irrational number, as it cannot be expressed in the form of p/q.

### What is the value of cube of the cube root of 4?

The value of cube of the cube root of 4 is 4.
(i.e) Removing cube and cube root, we get
(∛4)3 = 4.

### What is the value of 4+ ∛4?

The value of 4+∛4 is 5.5874.
(i.e) we know that the value of cube root of 4 is 1.5874.
Hence, 4+∛4 = 4+1.5874 = 5.5874.

### Is 4 a perfect cube?

No, 4 is not a perfect cube, as it cannot be written in the form of the product of three equal integers.