Cube Root of 12

The cube root of 12 is a real number whose cube is 12. The cube root of 12 has a value that is roughly equal to 2.289. Finding the number’s cube root is the opposite of computing the number’s cube. The square root of an integer is often denoted by the radical sign “√” and the cube root is denoted by the radical sign “∛”. The notation 12^1/3 represents the cube root of 12 in exponential form. Let’s look at various methods for computing the cube root of 12.

Also, read: How to Find Cube Root?

What is the Cube Root of 12?

The cube root of 12 is the number whose cube is 12. The cube of an integer is a perfect cube. Because it is not able to be represented as the cube of any integer, 12 is not a perfect cube number. In this article, the cube root of 12 and the method for computing it are both explained.

Also, try out: Cube Root Calculator.

How to Find the Cube Root of 12?

Now, let’s determine the cube root of 12. Here, we’ll figure it out using several techniques.

Finding Cube Root of 12 by Prime Factorisation Method

The procedures for calculating a number’s cube root using the prime factorisation method are listed below.

• Determine the given number’s prime factors.
• For every prime factor in the prime factorisation, create a group of three.
• We take that factor once for each group before multiplying all the prime factors. If a factor cannot be divided into three, it cannot be further simplified.

Let’s try to use a prime factorisation technique to eventually calculate the cube root of 12.

We know that the prime factorisation of 12 is 2 × 2 × 3.

Therefore, this can be written as:

The cube root of 12 = ∛12 = ∛(2 × 2 × 3) = 2.289

Since ∛12 cannot be further reduced, and hence the cube root of 12 is also an irrational number.

Finding Cube Root of 12 by Approximation Method

Halley’s method, an approximation method, is used to find the cube root of any number. The cube root of 12 can be determined using Halley’s approach as follows:

Cube Root Calculation Using the Halley Formula:

Where,

The cube root that needs to be calculated is denoted by the letter “a”.

The estimated value, “x,” is often determined by taking the cube root of the closest perfect cube.

Here, a = 12

Suppose x = 2 and therefore, 2³ = 8 < 12

When these values are substituted in the Halley’s formula, we get a result that is very near to the cube root of 12.

∛12 = 2[(2³ + 2 × 12)/(2 × 2³ + 12)]

= 2[(8 + 24)/(16 + 12)]

= 2[32/28]

=2[1.1428] ≈ 2.29

This result is quite close to the actual cube root of 12.

Therefore, Halley’s approach yields a cube root of 12, which is equivalent to 2.29.

Video Lesson on Finding Cube Roots

Related Articles

• Cube Root Table
• Cube Root of 4
• Cube Root of 512
• Cube Root of 2
• Cube Root of Unity
• Cube Root of 729
• Cube Root of 9261

Solved Examples on Cube Root of 12

Example 1:

If ∛12x = 2.289, what is the value of x?

Solution:

Given equation: ∛12x = 2.289.

As we know, the cube root of 12 is approximately equal to 2.289.

When ∛12 = 2.289 is substituted into the preceding equation, the result is,

2.289 x = 2.289

⇒ x = 2.289/2.289

⇒ x = 1.

Hence, x has a value of 1.

Example 2:

Identify the smallest integer that must be multiplied by 12 to create a perfect cube number.

Solution:

As we know, the prime factorisation of 12 is 2 × 2 × 3.

To find the cube root of 12, we must group each factor by three. Consequently, we must multiply 12 by 2 × 3 × 3.

This means that 12 × 2 × 9 = 12 × 18 = 216 is a perfect cube number.

So, the cube root of 216 is ∛(2 × 2 × 2 × 3 × 3 × 3) = 2 × 3 = 6

Therefore, the smallest integer that must be multiplied by 12 to create a perfect cube number is 18.

Example 3:

If a cube’s volume is 12 cm³, determine its sides’ length.

Solution:

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

The cube’s volume is therefore equal to x³ = 12 cm³.

Now, take the cube root on both sides, and we get,

⇒ x = ∛12 = 2.289 cm approximately.