Cube Root of 17

The real number whose cube is 17 is the cube root of 17. The value of the cube root of 17 is about 2.571. The reverse of computing a number’s cube is finding its cube root. The radical signs “√” and “∛” are frequently used to represent the square root and cube root, respectively. The exponential version of the cube root of 17 is represented by the notation 17^1/3. Let’s explore numerous approaches of finding the cube root of 17.

Also, read: How to Find Cube Root?

What is the Cube Root of 17?

The number whose cube is 17 is the cube root of 17. A perfect cube is an integer’s cube. 17 is not a perfect cube number since it cannot be written as the cube of any integer. Also, the number 17 is a prime number. The cube root of 17 and how to compute it are described in this article.

Also, try out: Cube Root Calculator.

How to Find the Cube Root of 17?

Let’s now calculate the cube root of 17. Here, we’ll solve it through a variety of methods.

Finding Cube Root of 17 by Prime Factorisation Method

The steps for applying the prime factorisation method to determine the cube root of a number are outlined below.

• Find the prime factors that make up the given number.
• Make a group of three for each prime factor in the prime factorisation.
• Preceding the multiplication of all the prime factors, we take that factor once for each group. A factor cannot be further simplified if it cannot be broken into three.

Let’s try calculating the cube root of 17 using a prime factorisation method.

We know that the prime factorisation of 17 is 1 × 17.

Hence, this can be written as:

The cube root of 17 = ∛(1 × 17) = ∛17 = 2.571

Since ∛17 cannot be reduced further, its cube root also has an irrational value.

Also, read: Irrational Number.

Finding Cube Root of 17 by Approximation Method

The cube root of any number can be determined using Halley’s approach, also known as an approximation technique. Using Halley’s method, the cube root of 17 can be found as follows:

Cube Root Calculation Using the Halley Formula:

Where

The letter “a” denotes the cube root that must be calculated.

The estimated value, “x,” is calculated by taking the cube root of the nearest perfect cube.

Here, a = 17

Assume that x = 2 and, therefore, we get, 2³ = 8 < 17

We obtain a result that is extremely close to the cube root of 17 when these numbers are inserted in Halley’s formula:

∛17 = 2[(2³ + 2 × 17)/(2 × 2³ + 17)]

= 2[(8 + 34)/(16 + 17)]

= 2[42/33]

=2[1.272] ≈ 2.54

This outcome comes quite near to the cube root of 17.

Halley’s method produces a cube root of 17, which is equal to 2.54, as a result.

Video Lesson on Finding Cube Roots

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Solved Examples on Cube Root of 17

Example 1:

If ∛17x = 2.571, what is the value of x?

Solution:

Given equation: ∛17x = 2.571.

We already know that the cube root of 17 is roughly equivalent to 2.571.

When ∛17 = 2.571 is inserted into the given equation, the result is,

2.571 x = 2.571

⇒ x = 2.571 / 2.571

⇒ x = 1.

Hence, x = 1.

Example 2:

Find the smallest integer that needs to be multiplied by 17 in order to produce the perfect cube number.

Solution:

As it is known that, the prime factorisation of 17 is 1 × 17.

Each factor must be grouped by three in order to determine the cube root of 17. Therefore, we need to multiply 17 by 17 × 17.

This proves that the perfect cube number is 4913. (i.e., 17 × 17 × 17 = 17 × 289 = 4913)

So, the cube root of 4913 is ∛(17 × 17 × 17) = 17

As a result, 289 is the smallest number that can be multiplied by 17 to produce a perfect cube number.

Example 3:

Calculate the length of a cube’s sides if its volume is 17 cm³.

Solution:

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

Therefore, the cube’s volume is equal to a³ = 17 cm³.

Taking the cube root now on both sides, we obtain

⇒ a = ∛17 = 2.571 cm approximately.