What is the smallest number that 5 500 must be multiplied by to make it a perfect square?

A natural number whose cube is 500 is known as the cube root of 500. The cube root of 500 is about 7.937. The process of finding the cube root of an integer is the inverse of cubing that number. The radicals “√” and “∛”, respectively, stand for the square root and cube root. The number 5001/3 represents the cube root of 500 exponentially. Let’s examine several methods for determining the cube root of 500.

Nội dung chính Show

• What is the Cube Root of 500?
• Finding Cube Root of 500 by Prime Factorisation Method
• Finding Cube Root of 500 by Approximation Method
• Video Lesson on Finding Cube Roots
• Related Articles
• Solved Examples on Cube Root of 500
• Frequently Asked Questions on Cube Root of 500
• What do you get when you take the cube root of 500?
• What do you think of the number 500? Is it an exact cube number?
• What does the cube root of -500 equal?
• What is the sum you obtain when you take the cube root of 500 and add it to 10?
• What is the most simple radical expression of the cube root of 500?
• What should be multiplied to 500 to make it a perfect cube?
• What is the smallest number by which 500 may be multiplied to get a perfect square?
• IS 500 a perfect square cube?
• What is the smallest number that must be multiplied with 5400 to make it a perfect cube?

Also, read:How to Find Cube Root?

What is the Cube Root of 500?

The number whose cube is 500 is known as the cube root of 500. A perfect cube is always produced by the cube of an integer. 500 is not a perfect cube number since it is not the cube of any integer. 500 is a composite number as well. This article provides a full explanation of how to calculate the cube root of 500.

Also, try out:Cube Root Calculator.

Now let’s calculate the 500’s cube root. We’ll examine it from various angles in this article.

Finding Cube Root of 500 by Prime Factorisation Method

The steps for using the prime factorisation method to get the cube root of an integer are described below.

• Find the number’s prime factors.
• For every prime factor in the prime factorization, create a group of three.
• One occurrence of the factor is chosen for each group, and all 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 get the cube root of 500.

As it is well known, the prime factorisation of 500 is 2 × 2 × 5 × 5 × 5.

Consequently, the following is the radical representation of 500’s cube root:

∛500 = ∛( 2 × 2 × 5 × 5 × 5) = 5 × ∛4 = 5∛4.

Because the number 5∛4 cannot be lowered any further, the cube root of 500 is also an irrational number.

Finding Cube Root of 500 by Approximation Method

Any number’s cube root may be found using Halley’s technique, sometimes referred to as an approximation method. The cube root of 500 may be calculated using Halley’s method as shown below:

Halley’s Cube Root Formula:

\(\begin{array}{l}\sqrt[3]{a}\approx x\left [ \frac{x^{3}+2a}{2x^{3}+a} \right ]\end{array} \)

Where

The computation that must be performed in order to get the cube root is denoted by the alphabet “a.”

The cube root of the nearest perfect cube, “x,” should be employed to calculate the predicted value.

Here, a = 500

The result will be 73 = 343 < 500 for x = 7.

The result of finding the square root of 500 using Halley’s formula is very similar to the actual cube root value.

∛500 = 7[(73 + 2 × 500)/(2 × 73 + 500)]

∛500 = 7[(343 + 1000)/(686 + 500)]

∛500 = 7[1343/1186]

∛500 = 7[1.1323] ≈ 7.926, which is roughly equal to the cube root of 500.

With the use of the Halley formula, we can determine that the cube root of 500 is 7.926.

Video Lesson on Finding Cube Roots

Related Articles

• Cube Root 1 to 20
• Cube Root Table
• Cube Root of 1 to 30
• Cube Root of Unity
• Cube Root of 4
• Cube Root of 9261
• Cube Root of 2

Solved Examples on Cube Root of 500

Example 1:

If the equation ∛500x = 13(7.937) is true, determine the value of x.

Solution:

Equation given: ∛500x = 13(7.937).

It is commonly known that the cube root of 500 is quite close to the number 7.937.

The solution is obtained by entering the number ∛500 = 7.937 into the previously stated equation.

7.937 x = 13(7.937)

⇒ x = [13(7.937)] /7.937

⇒ x = 13.

Consequently, x = 13

Example 2:

Find the smallest integer that results in a perfect cube when multiplied by 500.

Solution:

As we already know, the prime factorisation of 500 is 2 × 2 × 5 × 5 × 5.

It is necessary to first group each element by three before calculating the cube root of 500. We must then multiply 500 by 2 as a result.

Consequently, we get

500 × 2 = 1000

As a result, 1000 is the perfect cube number.

Thus, the cube root of 1000 is ∛(2 × 2 × 2 × 5 × 5 × 5 ) = 2 × 5 = 10

As a consequence, 2 is the least number that can be multiplied by 500 to get the perfect cube number.

Example 3:

Determine the lengths of the sides of the cube, given that its volume is 500 cm3.

Solution:

If “a” represents the length of one of the cube’s sides, then the following is the solution:

This indicates that a3 = 500 cm3 is the cube’s volume.

The result is obtained by calculating the cube roots on both sides of the problem.

a = ∛500 = 7.937 (approximately).

Therefore, the value of the variable “a” is about 7.937.

Frequently Asked Questions on Cube Root of 500