Cube Root of 30

A natural number whose cube is 30 is called the cube root of 30. The cube root of 30 is around 3.107. The opposite of cubing an integer is calculating its cube root. The radical symbols “√” and “∛”, which stand for the square root and cube root, respectively. Exponentially, 30^1/3 represents the cube root of 30. Let’s examine various methods for calculating the cube root of 30.

Also, read:How to Find Cube Root?

What is the Cube Root of 30?

The number whose cube is 30 is known as the cube root of 30. A perfect cube is an integer’s cube. 30 is not a perfect cube number since it is not the cube of any integer. 30 is also a composite number. This article thoroughly explains how to compute the cube root of 30.

Also, try out:Cube Root Calculator.

How to Find the Cube Root of 30?

Now let’s calculate the cube root of 30. In this article, we’ll discuss it in a number of ways.

Finding Cube Root of 30 by Prime Factorisation Method

Below is a list of the steps involved in using the prime factorisation method to calculate an integer’s cube root.

• Find the number’s prime factors.
• To every prime factor in the prime factorisation, create a group of three.
• Before multiplying all of the prime factors, just one occurrence of the factor is chosen for each group. If a factor cannot be divided into three, it cannot be further simplified.

Let’s use the prime factorisation method to calculate the cube root of 30.

As is well known, the prime factorisation of 30 is 2 × 3 × 5.

Therefore, the cube root of 30 is:

= ∛(2 × 3 × 5) = ∛30

As ∛30 cannot be reduced further, then the result for the cube root of 30 is an irrational number as well.

Finding Cube Root of 30 by Approximation Method

Halley’s technique, often known as an approximation method, allows us to get the cube root of any number. The cube root of 30 may be calculated using Halley’s approach, as shown below:

Halley’s Cube Root Formula: ∛a ≈ x[(x³ + 2a)/(2x³ + a)]

Where

The letter “a” stands in for the required cube root computation.

Take the cube root of the nearest perfect cube, “x,” to obtain the estimated value.

In this instance, a equals 30. I.e., a = 30.

Substitute x = 3, and hence we get 3³ = 27 < 30

The cube root of 30 is computed using Halley’s formula, and the result comes out quite similar to it.

∛30 = 3[(3³ + 2 × 30)/(2 × 3³ + 30)]

∛30 = 3[(27 + 60)/(54 + 30)]

∛30 = 3[87/84]

∛30 = 3[1.0357] ≈ 3.1071, is quite close to the cube root of 30.

Using Halley’s formula, the cube root of 30 is found to be 3.1071.

Video Lesson on Finding Cube Roots

Related Articles

• Cube Root of 2
• Cube Root of 216
• Cube Root Table
• Cube Root 1 to 20
• Cube Root of Unity
• Cube Root 1 to 30
• Cube Root of 729

Solved Examples on Cube Root of 30

Example 1:

If ∛30x = 7 (3.107), determine the value of x.

Solution:

The equation given is ∛30x = 7 (3.107).

As we know, the cube root of 30 equals 3.107.

When ∛30 = 3.107 is substituted in the given equation, we obtain

3.107 x = 7 (3.107)

⇒ x = [7(3.107)] / 3.107

⇒ x = 7.

Hence, x has a value of 7.

Example 2:

To create a perfect cube number, identify the smallest integer that can be multiplied by 30.

Solution:

As we know, the prime factorisation of 30 is 2 × 3 × 5.

To find the cube root of 30, each element must be grouped by three. As a result, we must multiply 30 by 2 × 2 × 3 × 3 × 5 × 5.

Consequently, we have

30 × 2 × 2 × 3 × 3 × 5 × 5 = 30 × 900 = 27000

Therefore, 27000 is a perfect cube number.

The cube root of 27000 is thus, ∛(2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5 ) = 2 × 3 × 5 = 30

Hence, the smallest number that may be multiplied by 30 to get the perfect cube number is 900.

Example 3:

Calculate the side lengths of a cube with a volume of 30 cm³.

Solution:

Consider the cube’s side length to be “a.”

The volume of the cube is therefore equal to a³ = 30 cm³.

When we now take the cube roots of the two sides of the equation, we get

⇒ a = ∛30 = 3.107 cm (approx).

The value of “a” is therefore around 3.107.