Cube Root of 13

The natural number whose cube is 13 is the cube root of 13. The cube root of 13 is around 2.351. Cubing an integer is the opposite of calculating its cube root. The radical symbols “√” and “∛” are used to indicate the square root and cube root, respectively. The exponential representation of the cube root of 13 is 13^1/3. Let’s examine various methods for finding the cube root of 13.

Also, read: How to Find Cube Root?

What is the Cube Root of 13?

The number whose cube is 13 is referred to as 13’s cube root. An integer’s cube is a perfect cube. 13 is not a perfect cube number since it is not the cube of any integer. 13 is also a prime number. In this article, the cube root of 13 and its calculation are explained.

Also, try out: Cube Root Calculator.

How to Find the Cube Root of 13?

Now, let’s compute the cube root of 13. In this article, we’ll cover it in a variety of ways.

Finding Cube Root of 13 by Prime Factorisation Method

Below are the procedures for finding the cube root of an integer using the prime factorisation technique.

• Determine the integer’s prime factors.
• In the prime factorization, create a group of three for each prime factor.
• Before multiplying all the prime factors, just one occurrence of the factor is taken for each group. If a factor cannot be divided into three, it cannot be further simplified.

To find the cube root of 13, let’s continue using the prime factorisation technique.

1 × 13 is recognised as a prime factorisation of 13.

Therefore, the cube root of 13 is:

= ∛(1 × 13) = ∛13

13 cannot be reduced further. Consequently, its cube root is likewise an irrational number.

Finding Cube Root of 13 by Approximation Method

Using Halley’s technique, commonly known as an approximation method, it is possible to determine the cube root of any integer. Using Halley’s approach, one may find the cube root of 13 as follows:

Halley’s Cube Root Formula:

Where

The letter “a” represents the required cube root calculation.

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

In this case, a equals 13. I.e., a = 13.

Assuming x = 2, we get 2³ = 8 < 13

When these values are plugged into Halley’s formula, the result is quite close to the cube root of 13.

∛13 = 2[(2³ + 2 × 13)/(2 × 2³ + 13)]

∛13 = 2[(8 + 26)/(16 + 13)]

∛13 = 2[34/29]

∛13 = 2[1.1724] ≈ 2.34, which is close to 13’s cube root.

Using Halley’s formula, the cube root of 13 is found to be 2.34.

Video Lesson on Finding Cube Roots

Related Articles

• Cube Root Table
• Cube Root of 2
• Cube Root 1 to 20
• Cube Root of 3
• Cube Root of Unity
• Cube Root 1 to 30
• Cube Root of 4

Solved Examples on Cube Root of 13

Example 1:

Determine x’s value if ∛13x = 3 (2.351).

Solution:

Given equation: ∛13x = 3 (2.351).

We are aware that the cube root of 13 is roughly 2.351.

When ∛13 = 2.351 is substituted into the above-given equation, we obtain

2.351 x = 3(2.351)

⇒ x = [3(2.351)] / 2.351

⇒ x = 3.

Therefore, x has a value of 3.

Example 2:

Determine the lowest integer that can be multiplied by 13 to get the perfect cube number.

Solution:

As is commonly known, the prime factorisation of 13 is 1 × 13.

To compute the cube root of 13, each element must be grouped by three. Consequently, we must multiply 13 by 13 × 13.

Therefore, we get

13 × 13 × 13 = 13 × 169 = 2197

Hence, 2197 is a perfect cube number.

So, the cube root of 2197 is ∛(13 × 13 × 13 ) = 13.

Therefore, 169 is the least number that can be multiplied by 13 to get the perfect cube number.

Example 3:

Determine the length of the sides of a cube whose volume is 13 cm³.

Solution:

Consider “a” as the side length of the cube.

Accordingly, the volume of the cube is equal to a³ = 13 cm³.

Now, take the cube roots on both sides of the equation, and we get

⇒ a = ∛13 = 2.351 cm (approx).

Therefore, the value of a is approximately equal to 2.351.