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 30.33. 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 ofa = ((x3 + 2a)/(2x3 + 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 13 = 1 and 1 is the closest perfect cube to 3).

Thus, with x = 1:

Cube root of 3 ≈ ((13 + 2 × 3)/(2 × 13 + 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.