# Value of Root 3

## Value of root 3

The cube root of 3, rounded to six decimal places, is 1.44225. This value satisfies the equation x³ = 3. In radical notation, the cube root of 3 is represented as Cube root of 3, while in exponential notation, it is written as 3^{(1/3)} or 3^{0.33}. Since the prime factorization of 3 is simply 3, the simplest radical form of the cube root of 3 remains Cube root of 3.

- Cube root of 3: 1.44224957
- Cube root of 3 in Exponential Form: 3
^{(1/3)} - Cube root of 3 in Radical Form:Cube root of3

### What is the Cube Root of 3?

The cube root of three is the value that, when multiplied by itself twice more, results in three. Since three is a prime number, its cube root equals approximately 1.4422.

### How to Calculate the Value of the Cube Root of 3?

To find the cube root of a number *a* using Halley's method, we use the formula:

Cube root of*a* = ((*x*^{3} + 2*a*)/(2*x*^{3} + *a*))

where *a* is the number for which the cube root is being calculated, and *x* is an estimate of the cube root.

For *a = 3*, we start with *x = 1* (since 1^{3} = 1 and 1 is the closest perfect cube to 3).

Thus, with *x = 1*:

Cube root of 3 ≈ ((1^{3} + 2 × 3)/(2 × 1^{3} + 3)) = (1 + 6)/(2 + 3) = 7/5 = 1.4

Therefore, the cube root of 3 is approximately 1.4.

### Is the Cube Root of 3 Irrational?

Yes, because the number 3 cannot be expressed as a fraction p/q where q is a negative number. Therefore, the cube root of 3 is considered an irrational number.

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## Frequently Asked Questions on Value of Root 3

√3 is approximately equal to 1.73205081, which is a mathematical constant that represents the square root of the number 3. It is an irrational number, meaning its decimal representation never ends or repeats.

To find √3, you can use a calculator, as shown in the search result. Alternatively, you can use the formula √3 = 1 + 2/3 + 2/9 + 2/27 + ... to approximate the value of √3 to any desired accuracy.

√2 is approximately equal to 1.41421356, which is another mathematical constant that represents the square root of the number 2. Like √3, √2 is also an irrational number.

The value of √3 is approximately 1.73205081. The symbol "√" is used to represent the square root operation, and "3" is the number whose square root is being calculated.

There is no single formula for √3, as it is an irrational number. However, you can use the formula √3 = 1 + 2/3 + 2/9 + 2/27 + ... to approximate its value to any desired accuracy. Additionally, you can use a calculator to find the square root of 3.