Cube Root of 15

The cube root of 15 is a natural number whose cube is 15. 15 has a cube root of about 2.466. Calculating an integer’s cube root is the reverse of cubing it. The square root and cube root are denoted by the radical symbols “√” and “∛”, respectively. The cube root of 15 is represented exponentially by 15^1/3. Let’s look at different approaches to determine the cube root of 15.

Also, read:How to Find Cube Root?

What is the Cube Root of 15?

The cube root of 15 is the number whose cube is 15. The cube of an integer is a perfect cube. Since 15 is not the cube of any integer, it is not a perfect cube number. 15 is a composite number as well. This article explains how to calculate the cube root of 15 in detail.

Also, try out:Cube Root Calculator.

How to Find the Cube Root of 15?

Let’s now determine the cube root of 15. We’ll discuss it in a variety of ways in this article.

Finding Cube Root of 15 by Prime Factorisation Method

The steps for employing the prime factorisation method to determine the cube root of an integer are listed below.

• Find the prime factors of the number.
• Make a group of three for each prime factor in the prime factorisation.
• For each group, only one occurrence of the factor is taken before multiplying all of the prime factors. A factor cannot be further simplified if it cannot be broken into three.

Let’s proceed with the prime factorisation technique to determine the cube root of 15.

As we know, the prime factorisation of 15 is 3 × 5.

Hence, the cube root of 15 is:

= ∛(3 × 5) = ∛15

The number 15 cannot be reduced even further. As a result, its cube root is an irrational number as well.

Finding Cube Root of 15 by Approximation Method

Any integer’s cube root can be found using Halley’s approach, also referred to as an approximation method. Halley’s method can be used to determine the cube root of 15 as shown below:

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

Where

The appropriate cube root computation is represented by the letter “a”.

To get the estimated value, take the cube root of the closest perfect cube, “x”.

In this case, a equals 15. I.e., a = 15.

If x = 2, we get 2³ = 8 < 15

Halley’s formula is used to calculate these values, and the outcome is fairly close to the cube root of 15.

∛15 = 2[(2³ + 2 × 15)/(2 × 2³ + 15)]

∛15 = 2[(8 + 30)/(16 + 15)]

∛15 = 2[38/31]

∛15 = 2[1.225] ≈ 2.45, which is near to cube root of 15.

The cube root of 15 is calculated to be 2.45 using Halley’s formula.

Video Lesson on Finding Cube Roots

Related Articles

• Cube Root of 2
• Cube Root Table
• Cube Root of 3
• Cube Root 1 to 20
• Cube Root 1 to 30
• Cube Root of Unity

Solved Examples on Cube Root of 15

Example 1:

Calculate the value of x if ∛15x = 10 (2.466).

Solution:

Given equation: ∛15x = 2.466.

We know that the cube root of 15 is around 2.466.

If ∛15 = 2.466 is substituted in the above given equation, we get

2.466 x = 10 (2.466)

⇒ x = [10(2.466)] / 2.466

⇒ x = 10.

Hence, the value of x is 10.

Example 2:

Find the smallest integer that can be multiplied by 15 to obtain a perfect cube number.

Solution:

The prime factorisation of 15 is 3 × 5.

Every element must be grouped by three in order to calculate the cube root of 15. Therefore, we need to multiply 15 by 3 × 3 × 5 × 5.

As a result, we have

15 × 3 × 3 × 5 × 5 = 15 × 225 = 3375

Therefore, a perfect cube number is 3375.

Therefore, 3375’s cube root is ∛(3 × 3 × 3 × 5 × 5 × 5 ) = 3 × 5 = 15

In order to obtain the perfect cube number, the least number that may be multiplied by 15 is 225.

Example 3:

Identify the lengths of the sides of a 15 cm³ cube.

Solution:

Take “a” to represent the cube’s side length.

As a result, the cube’s volume equals a³ = 15 cm³.

Taking the cube roots of the two sides of the equation now, we obtain

⇒ a = ∛15 = 2.466 cm (approx).

As a result, “a” has a value that is roughly 2.466.