Dividing 8748 by the Smallest Number to Get a Perfect Cube Quotient

Oct 13, 2025 by wbrum.org 144 views

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Introduction

In mathematics, perfect cubes are numbers that can be expressed as the cube of an integer. For instance, 27 is a perfect cube because it can be expressed as 3^3. In this article, we will explore the concept of perfect cubes and how to divide a given number by the smallest number to obtain a perfect cube quotient. We will also find the cube root of the quotient.

What are Perfect Cubes?

Perfect cubes are numbers that can be expressed as the cube of an integer. For example, 1, 8, 27, 64, and 125 are perfect cubes because they can be expressed as 1^3, 2^3, 3^3, 4^3, and 5^3, respectively. Perfect cubes have the property that their cube root is an integer.

Dividing 8748 by the Smallest Number to Get a Perfect Cube Quotient

To divide 8748 by the smallest number to get a perfect cube quotient, we need to find the prime factorization of 8748. The prime factorization of 8748 is:

8748 = 2^3 × 3^3 × 7^2

Finding the Smallest Number to Divide 8748

To find the smallest number to divide 8748, we need to find the smallest number that can be multiplied by 8748 to get a perfect cube. We can do this by finding the smallest number that can be multiplied by 8748 to get a perfect cube.

Finding the Smallest Number to Multiply 8748

To find the smallest number to multiply 8748, we need to find the smallest number that can be multiplied by 8748 to get a perfect cube. We can do this by finding the smallest number that can be multiplied by 8748 to get a perfect cube.

Finding the Smallest Number to Multiply 8748

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Frequently Asked Questions

Q: What is a perfect cube?

A: A perfect cube is a number that can be expressed as the cube of an integer. For example, 1, 8, 27, 64, and 125 are perfect cubes because they can be expressed as 1^3, 2^3, 3^3, 4^3, and 5^3, respectively.

Q: How do I find the smallest number to divide 8748 to get a perfect cube quotient?

A: To find the smallest number to divide 8748, you need to find the prime factorization of 8748. The prime factorization of 8748 is 2^3 × 3^3 × 7^2. Then, you need to find the smallest number that can be multiplied by 8748 to get a perfect cube.

Q: What is the smallest number that can be multiplied by 8748 to get a perfect cube?

A: The smallest number that can be multiplied by 8748 to get a perfect cube is 7^2, which is 49.

Q: How do I find the cube root of the quotient?

A: To find the cube root of the quotient, you need to divide 8748 by 49, which gives you 178. Then, you need to find the cube root of 178.

Q: What is the cube root of 178?

A: The cube root of 178 is not an integer, but it can be expressed as a decimal number.

Q: Why is the cube root of 178 not an integer?

A: The cube root of 178 is not an integer because 178 is not a perfect cube. However, you can express the cube root of 178 as a decimal number.

Q: How do I express the cube root of 178 as a decimal number?

A: To express the cube root of 178 as a decimal number, you can use a calculator or a computer program to find the decimal approximation of the cube root of 178.

Q: What is the decimal approximation of the cube root of 178?

A: The decimal approximation of the cube root of 178 is 5.31.

Q: Why is it important to find the cube root of the quotient?

A: Finding the cube root of the quotient is important because it helps you to understand the properties of perfect cubes and how to divide numbers to get perfect cube quotients.

Q: Can you give an example of how to use the concept of perfect cubes in real-life situations?

A: Yes, here's an example: Imagine you have a box of 8748 cubes, and you want to stack them up in a way that each layer has the same number of cubes. If you divide 8748 by the smallest number to get a perfect cube quotient, you can find the number of cubes in each layer.

Q: How do I apply the concept of perfect cubes in real-life situations?

A: To apply the concept of perfect cubes in real-life situations, you need to understand how to find the smallest number to divide a number to get a perfect cube quotient and how to find the cube root of the quotient.

Q: What are some common applications of perfect cubes in mathematics and real-life situations?

A: Some common applications of perfect cubes in mathematics and real-life situations include:

Finding the volume of a cube
Finding the surface area of a cube
Finding the diagonal of a cube
Finding the number of cubes in a stack
Finding the number of layers in a stack of cubes

Q: Can you give an example of how to use the concept of perfect cubes to find the volume of a cube?

A: Yes, here's an example: Imagine you have a cube with a side length of 5 units. To find the volume of the cube, you need to find the cube of the side length, which is 5^3 = 125 cubic units.

Q: How do I find the cube of a number?

A: To find the cube of a number, you need to multiply the number by itself three times. For example, to find the cube of 5, you need to multiply 5 by itself three times: 5 × 5 × 5 = 125.

Q: What are some common mistakes to avoid when working with perfect cubes?

A: Some common mistakes to avoid when working with perfect cubes include:

Not understanding the concept of perfect cubes
Not finding the smallest number to divide a number to get a perfect cube quotient
Not finding the cube root of the quotient
Not applying the concept of perfect cubes in real-life situations
Not checking for errors when working with perfect cubes

Q: How do I avoid common mistakes when working with perfect cubes?

A: To avoid common mistakes when working with perfect cubes, you need to understand the concept of perfect cubes, find the smallest number to divide a number to get a perfect cube quotient, find the cube root of the quotient, and apply the concept of perfect cubes in real-life situations.