Cube Root of 6

A natural number whose cube is 6 is called the cube root of 6. The cube root of 6 is equal to 1.817 approximately. The opposite of cubing an integer is to find its cube root. The radicals “√” and “∛” respectively, stand for the square root and cube root. The number 6^1/3 serves as an exponential representation of the cube root of 6. Let’s examine various methods for determining the cube root of 6.

Also, read:How to Find Cube Root?

What is the Cube Root of 6?

The number whose cube is 6 is the cube root of 6. An integer’s cube always results in a perfect cube. 6 is not a perfect cube number since it is not the cube of any integer. Six is a composite number as well. This article provides a full explanation of how to calculate the cube root of 6.

Also, try out:Cube Root Calculator.

How to Find the Cube Root of 6?

Now let’s calculate the cube root of 6. We’ll examine it from a number of approaches in this article.

Finding Cube Root of 6 by Prime Factorisation Method

The steps to get the cube root of an integer using the prime factorization method are listed below.

• Find the number’s prime factors.
• For every prime factor in the prime factorization, make a group of three.
• A single occurrence of the factor is chosen on every group, and then all the prime factors are multiplied. If a factor cannot be divided into three, it cannot be further simplified.

Applying the prime factorization technique, let’s calculate the cube root of 6.

As we know, the prime factorisation of 6 is 2 × 3.

As a result, the cube root of 6 in radical form is:

∛6 = ∛(2 × 3).

Since ∛6 cannot be further reduced, its cube root is an irrational number as well.

Finding Cube Root of 6 by Approximation Method

The cube root of any number may be obtained using Halley’s technique, which is sometimes referred to as an approximation method. The cube root of 6 can be calculated using Halley’s method as shown below:

Halley’s Cube Root Formula:

Where

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

Take the cube root of the nearest perfect cube, “x,” to get the projected value.

Here, a = 6

1³ = 1 < 6, will be obtained, if x = 1.

The cube root of 6 is computed using Halley’s formula, and the outcomes are quite similar.

∛6 = 1[(1³ + 2 × 6)/(2 × 1³ + 6)]

∛6 = 1[(1 + 12)/(2 + 6)]

∛6 = 1[13/8]

∛6 = 1[1.625] ≈ 1.625, which is close to 6’s cube root.

Using Halley’s formula, we can determine that 1.625 is the cube root of 6.

Video Lesson on Finding Cube Roots

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• Cube Root Table
• Cube Root of 64
• Cube Root of 4

Solved Examples on Cube Root of 6

Example 1:

Find x’s value, if ∛6x = 9(1.817).

Solution:

Equation given: ∛6x = 9(1.817).

We already know that 1.817 is almost equivalent to the cube root of 6.

If the value ∛6 = 1.817 is substituted into the equation above, the result is,

1.817 x = 9(1.817)

⇒ x = [9(1.817)] /1.817

⇒ x = 9

Therefore, x equals 9.

Example 2:

Determine the smallest integer that, when multiplied by 6, generates a perfect cube number

Solution:

As it is well known, 2 × 3 is the prime factorization of 6.

To get the cube root of 6, each factor must be grouped by three. As a result, we must multiply 6 by 2 × 2 × 3 × 3.

This gives us,

6 × 2 × 2 × 3 × 3 = 6 × 4 × 9 = 6 × 36 = 216

Hence, the number 216 is a perfect cube number.

As a result, the cube root of 216 is ∛(2 × 2 × 2 × 3 × 3 × 3 ) = 2 × 3 = 6

Hence, the smallest number that may be multiplied by 6 to obtain the perfect cube number is 36.

Example 3:

Determine the dimensions of the sides of a cube with a 6 cm³ volume.

Solution:

Assuming “a” represents the cube’s side length.

This indicates that a³ = 6 cm³ is the cube’s volume.

By computing the cube roots on both sides of the equation, we arrive at

a = ∛6 = 1.817 (approximately).

The value of “a” is thus around 1.817.