Cube Root of 36

A natural number whose cube is 36 is called the cube root of 36. The cube root of 36 is about 3.3019. The opposite of cubing an integer is to get its cube root. The radical symbols “√” and “∛”, respectively, stand for the square root and cube root. 36^1/3 is an exponential representation of the cube root of 36. Let’s examine various methods for determining the cube root of 36.

Also, read:How to Find Cube Root?

What is the Cube Root of 36?

The value whose cube is 36 is known as the cube root of 36. A perfect cube is the cube of an integer. 36 is not a perfect cube number since it is not the cube of any integer. Further, 36 is a composite number. This article provides a detailed explanation of how to calculate the cube root of 36.

Also, try out:Cube Root Calculator

How to Find the Cube Root of 36?

Now let’s find the 36’s cube root.

Finding Cube Root of 36 by Prime Factorisation Method

The prime factorisation method may be used to determine the cube root of an integer, as described in the list of operations below.

• Find the number’s prime factors.
• To every prime factor in the prime factorisation, create a group of three.
• For each group, just one instance of the factor is chosen, and all of the prime factors are then multiplied. If a factor cannot be divided into three, it cannot be further simplified.

Let’s use the prime factorisation technique to find 36’s cube root.

As we know, the prime factorisation of 36 is 2 × 2 × 3 × 3.

Thus, the cube root of 36 is:

= ∛(2 × 2 × 3 × 3) = ∛36

The cube root of 36 is likewise an irrational number as ∛36 cannot be reduced further.

Finding Cube Root of 36 by Approximation Method

We may use Halley’s technique, which is also known as an approximation method, to find the cube root of any number. The cube root of 36 may be calculated using Halley’s approach 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 obtain the estimated value.

In this scenario, a = 36

If we use x = 3, we will have 3³ = 27 < 36

The cube root of 36 is computed using Halley’s formula, and the outcome is quite comparable.

∛36 = 3[(3³ + 2 × 36)/(2 × 3³ + 36)]

∛36 = 3[(27 + 72)/(54 + 36)]

∛36 = 3[99/90]

∛36 = 3[1.1] ≈ 3.3, which is very close to 36’s cube root.

Using Halley’s formula, the cube root of 36 is found to be 3.3.

Video Lesson on Finding Cube Roots

Related Articles

• Cube Root Table
• Cube Root of Unity
• Cube Root of 2
• Cube Root of 3
• Cube Root of 4
• Cube Root of 64
• Cube Root of 729
• Cube Root 1 to 20
• Cube Root 1 to 36

Solved Examples on Cube Root of 36

Example 1:

If ∛36x = 3 (3.3019), determine the value of x.

Solution:

Given: ∛36x = 3 (3.3019).

As we already know, 3.3019 is roughly equivalent to the cube root of 36.

If ∛36 = 3.3019 is substituted in the above equation, we obtain,

3.3019 x = 3 (3.3019)

⇒ x = [3(3.3019)] /3.3019

⇒ x = 3.

Thus, x equals 3.

Example 2:

Determine the lowest integer that, when multiplied by 36, results in a perfect cube number.

Solution:

It is commonly known that the prime factorisation of 36 is 2 × 2 × 3 × 3.

To determine the cube root of 36, each element must be grouped by three. As a result, we must multiply 36 by 2 × 3.

Consequently, we get,

36 × 2 × 3 = 36 × 6 = 216

As a result, 216 is a perfect cube number.

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

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

Example 3:

Estimate the side lengths of a cube with a 36 cm³ volume.

Solution:

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

The volume of the cube is therefore equal to a³ = 36 cm³.

By taking the cube roots on both sides of the equation, we get to a = ∛36 = 3.3019 (approximately).

As a result, “a” is roughly equal to 3.3019.