Cube Root of 3

Cube Root of 3 is approximately equal to 1.442. The radical form of the cube root of three is ∛3, and the exponential form is 3^1/3. Therefore, Finding the cube root of 3 is a little challenging even because it is not a perfect cube. In this article, we will learn to find the cube root of 3 by various methods.

Cube Root Definition

Cube Root of a number is a value that, when multiplied by itself thrice or three times, produces the original number.

For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27. Cube Root is denoted by “∛x” or “(x)^1/3. The cube root is used to find the side length of a cube if its volume is given and to solve cubic equations.

What is Cube Root of 3?

The cube root of 3 is approximately 1.44. Value of cube root of 3 accurate to first 10 decimal points is 1.4422495703.

∛3 = 1.44224957031

Cube Root Calculator

Cube root of any number can be calculated using the following calculator:

How to Find the Cube Root of 3?

To find the cube root of 3 various methods can be used that are given below:

• Cube Root of 3 by Halley’s Method

Cube Root of 3 by Halley’s Method

Halley’s Method is a root-finding algorithm that is also known as the tangent hyperbolas method or Halley’s rational formula. It can also be used to find the cube root of any number using the following formula:

∛a ≈ x × (x³ + 2a) / (2x³ + a)

where,

• ∛a represents Cube root of Number a you want to Find
• x is Initial Guess for Cube Root, usually the nearest integer less than or equal to the cube root of a.

a = 3 and x = 1 as [∛1 < ∛3 < ∛8].

∛3 ≈ 1 × (1³ + 2 × 3) / (2 × 1³ + 3)

⇒ ∛3 ≈ 1 × (1 + 6) / (2 + 3)

⇒ ∛3 ≈ 7/5 = 1.4

Thus, approximate value of cube root of 3 is 1.4.

Is Cube Root of 3 a Rational or Irrational Number?

The cube root of 3 is an irrational number. An irrational number is a number that cannot be expressed as a fraction of two integers, i.e., p/q where p and q are integers. Also, ∛3 has non-terminating decimal expansions which is sign for any number to be irrational number.

Some Facts about 3

Some general facts about the number 3:

• Three is the first odd prime number.
• It is the second triangular number.
• In Roman numerals, 3 is represented as III.
• Three is a Fibonacci number.
• In physics, our universe is commonly described as having three spatial dimensions: length, width, and height.
• In traditional color theory, there are three primary colors: red, blue, and yellow. These colors are fundamental because they can be combined to create all other colors.

Cube Root of 3: FAQs

What is the Value of the Cube Root of 3?

The cube root of 3 is 1.44225.

How to Represent Cube Root of 3?

Cube root of 3 is represented as ∛3 in radical form.

What is Cube of 3?

The value of cube of 3 is 27.

What methods can be used to find the Cube Root of 3?

We can use Halley’s method to find the cube root of 3.

What is the Value of Cube Root of Negative 3?

The cube root of -3 in approximate value is -1.442.