Cube of 679
2026-02-28 10:03 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-679

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Last updated on August 5, 2025

When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 679.

Cube of 679

A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times. When you cube a positive number, the result is always positive. When you cube a negative number, the result is always negative. This is because a negative number by itself three times results in a negative number. The cube of 679 can be written as \(679^3\), which is the exponential form. Or it can also be written in arithmetic form as, \(679 \times 679 \times 679\).

How to Calculate the Value of Cube of 679

In order to check whether a number is a cube number or not, we can use the following three methods, such as the multiplication method, a factor formula (\(a^3\)), or by using a calculator. These three methods will help you cube the numbers faster and easier without feeling confused or stuck while evaluating the answers. - By Multiplication Method - Using a Formula - Using a Calculator

By Multiplication Method

The multiplication method is a process in mathematics used to find the product of two numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts. Step 1: Write down the cube of the given number. \(679^3 = 679 \times 679 \times 679\) Step 2: You get 313,432,039 as the answer. Hence, the cube of 679 is 313,432,039.

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Using a Formula (\(a^3\))

The formula \((a + b)^3\) is a binomial formula for finding the cube of a number. The formula is expanded as \(a^3 + 3a^2b + 3ab^2 + b^3\). Step 1: Split the number 679 into two parts. Let \(a = 680\) and \(b = -1\), so \(a + b = 679\) Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) Step 3: Calculate each term \(a^3 = 680^3\) \(3a^2b = 3 \times 680^2 \times (-1)\) \(3ab^2 = 3 \times 680 \times (-1)^2\) \(b^3 = (-1)^3\) Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((680 - 1)^3 = 680^3 + 3 \times 680^2 \times (-1) + 3 \times 680 \times 1 + (-1)^3\) \(679^3 = 314,432,000 - 1,387,200 + 2,040 - 1\) \(679^3 = 313,432,039\) Step 5: Hence, the cube of 679 is 313,432,039.

Using a Calculator

To find the cube of 679 using a calculator, input the number 679 and use the cube function (if available) or multiply \(679 \times 679 \times 679\). This operation calculates the value of \(679^3\), resulting in 313,432,039. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 6, 7, followed by 9 Step 3: If the calculator has a cube function, press it to calculate \(679^3\). Step 4: If there is no cube function on the calculator, simply multiply 679 three times manually. Step 5: The calculator will display 313,432,039.

Tips and Tricks for the Cube of 679

The cube of any even number is always even, while the cube of any odd number is always odd. The product of two or more perfect cube numbers is always a perfect cube. A perfect cube can always be expressed as the product of three identical groups of equal prime factors.

Common Mistakes to Avoid When Calculating the Cube of 679

There are some typical errors that might occur during the process of cubing a number. Let us take a look at five of the major mistakes that might occur:

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Problem 1

What is the cube and cube root of 679?

Okay, lets begin

The cube of 679 is 313,432,039 and the cube root of 679 is approximately 8.82.

Explanation

First, let’s find the cube of 679. We know that the cube of a number is such that \(x^3 = y\) Where \(x\) is the given number, and \(y\) is the cubed value of that number So, we get \(679^3 = 313,432,039\) Next, we must find the cube root of 679 The cube root of a number \(x\) is such that \(\sqrt[3]{x} = y\) Where \(x\) is the given number, and \(y\) is the cube root value of the number So, we get \(\sqrt[3]{679} \approx 8.82\) Hence, the cube of 679 is 313,432,039 and the cube root of 679 is approximately 8.82.

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Problem 2

If the side length of a cube is 679 cm, what is the volume?

Okay, lets begin

The volume is 313,432,039 cm\(^3\).

Explanation

Use the volume formula for a cube \(V = \text{Side}^3\). Substitute 679 for the side length: \(V = 679^3 = 313,432,039\) cm\(^3\).

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Problem 3

How much larger is \(679^3\) than \(579^3\)?

Okay, lets begin

\(679^3 - 579^3 = 162,162,000\).

Explanation

First, find the cube of \(679^3\), that is 313,432,039. Next, find the cube of \(579^3\), which is 151,270,039. Now, find the difference between them using the subtraction method. 313,432,039 - 151,270,039 = 162,162,000. Therefore, \(679^3\) is 162,162,000 larger than \(579^3\).

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Problem 4

If a cube with a side length of 679 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 679 cm is 313,432,039 cm\(^3\).

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 679 means multiplying 679 by itself three times: First, calculate \(679 \times 679\) and then multiply the result by 679 again to get 313,432,039. The unit of volume is cubic centimeters (cm\(^3\)), because we are calculating the space inside the cube. Therefore, the volume of the cube is 313,432,039 cm\(^3\).

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Problem 5

Estimate the cube of 678 using the cube of 679.

Okay, lets begin

The cube of 678 is approximately 312,570,552.

Explanation

First, identify the cube of 679, The cube of 679 is \(679^3 = 313,432,039\). Since 678 is only a tiny bit less than 679, the cube of 678 will be slightly less than the cube of 679. The cube of 678 is approximately 312,570,552 because the difference between 678 and 679 is very small.

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FAQs on Cube of 679

1.What are the perfect cubes up to 679?

The perfect cubes up to 679 are 1, 8, 27, 64, 125, 216, 343, and 512.

2.How do you calculate \(679^3\)?

To calculate \(679^3\), use the multiplication method, \(679 \times 679 \times 679\), which equals 313,432,039.

3.What is the meaning of \(679^3\)?

\(679^3\) means 679 multiplied by itself three times, or \(679 \times 679 \times 679\).

4.What is the cube root of 679?

5.Is 679 a perfect cube?

No, 679 is not a perfect cube because no integer multiplied by itself three times equals 679.

Important Glossaries for Cube of 679

Binomial Formula: An algebraic expression used to expand the powers of a number, written as \((a + b)^n\), where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number. Cube of a Number: Multiplying a number by itself three times is called the cube of a number. Exponential Form: A way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, \(2^3\) represents \(2 \times 2 \times 2\) equals 8. Perfect Cube: A number that can be expressed as the cube of an integer. Cube Root: The value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2 because \(2 \times 2 \times 2 = 8\).

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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: He loves to play the quiz with kids through algebra to make kids love it.