Cube of 690
2026-02-28 08:57 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-690

199 Learners

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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 690.

Cube of 690

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 690 can be written as 690³, which is the exponential form. Or it can also be written in arithmetic form as, 690 × 690 × 690.

How to Calculate the Value of Cube of 690

In order to check whether a number is a cube number or not, we can use the following three methods, such as multiplication method, a factor formula (a³), or by using a calculator. These three methods will help kids to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.

  1. By Multiplication Method
  2. Using a Formula
  3. 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. 690³ = 690 × 690 × 690

Step 2: You get 328,509,000 as the answer. Hence, the cube of 690 is 328,509,000.

Explore Our Programs

Using a Formula (a³)

The formula (a + b)³ is a binomial formula for finding the cube of a number. The formula is expanded as a³ + 3a²b + 3ab² + b³.

Step 1: Split the number 690 into two parts, as and . Let a = 700 and b = -10, so a + b = 690

Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³

Step 3: Calculate each term

a³= 700³

3a²b = 3 × 700² × (-10)

3ab² = 3 × 700 × (-10)²

b³ = (-10)³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(700 - 10)³ = 700³ + 3 × 700² × (-10) + 3 × 700 × (-10)² + (-10)³

690³ = 343,000,000 - 147,000,000 + 210,000 - 1,000

690³ = 328,509,000

Step 5: Hence, the cube of 690 is 328,509,000.

Using a Calculator

To find the cube of 690 using a calculator, input the number 690 and use the cube function (if available) or multiply 690 × 690 × 690. This operation calculates the value of 690³, resulting in 328,509,000. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 6 followed by 9 and 0

Step 3: If the calculator has a cube function, press it to calculate 690³.

Step 4: If there is no cube function on the calculator, simply multiply 690 three times manually.

Step 5: The calculator will display 328,509,000.

Tips and Tricks for the Cube of 690

  • 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 690

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

Download Worksheets

Problem 1

What is the cube and cube root of 690?

Okay, lets begin

The cube of 690 is 328,509,000 and the cube root of 690 is approximately 8.879.

Explanation

First, let’s find the cube of 690.

We know that the cube of a number, such that x³ = y Where x is the given number, and y is the cubed value of that number

So, we get 690³ = 328,509,000

Next, we must find the cube root of 690 We know that the cube root of a number ‘x’, such that ∛x = y Where ‘x’ is the given number, and y is the cube root value of the number

So, we get ∛690 ≈ 8.879

Hence the cube of 690 is 328,509,000 and the cube root of 690 is approximately 8.879.

Well explained 👍

Problem 2

If the side length of the cube is 690 cm, what is the volume?

Okay, lets begin

The volume is 328,509,000 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 690 for the side length: V = 690³ = 328,509,000 cm³.

Well explained 👍

Problem 3

How much larger is 690³ than 400³?

Okay, lets begin

690³ – 400³ = 292,909,000.

Explanation

First find the cube of 690³, that is 328,509,000

Next, find the cube of 400³, which is 64,000,000

Now, find the difference between them using the subtraction method.

328,509,000 – 64,000,000 = 264,509,000

Therefore, the 690³ is 264,509,000 larger than 400³.

Well explained 👍

Problem 4

If a cube with a side length of 690 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 690 cm is 328,509,000 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).

Cubing 690 means multiplying 690 by itself three times: 690 × 690 = 476,100, and then 476,100 × 690 = 328,509,000.

The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.

Therefore, the volume of the cube is 328,509,000 cm³.

Well explained 👍

Problem 5

Estimate the cube 689.9 using the cube 690.

Okay, lets begin

The cube of 689.9 is approximately 328,509,000.

Explanation

First, identify the cube of 690, The cube of 690 is 690³ = 328,509,000.

Since 689.9 is only a tiny bit less than 690, the cube of 689.9 will be almost the same as the cube of 690.

The cube of 689.9 is approximately 328,509,000 because the difference between 689.9 and 690 is very small.

So, we can approximate the value as 328,509,000.

Well explained 👍

FAQs on Cube of 690

1.What are the perfect cubes up to 690?

The perfect cubes up to 690 are 1, 8, 27, 64, 125, 216, 343, 512, and 729.

2.How do you calculate 690³?

To calculate 690³, use the multiplication method, 690 × 690 × 690, which equals 328,509,000.

3.What is the meaning of 690³?

690³ means 690 multiplied by itself three times, or 690 × 690 × 690.

4.What is the cube root of 690?

5.Is 690 a perfect cube?

No, 690 is not a perfect cube because no integer multiplied by itself three times equals 690.

Important Glossaries for Cube of 690

  • 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, 2³ represents 2 × 2 × 2 equals 8.
  • Cube Root: The value that, when multiplied by itself three times, gives the original number.
  • Volume of a Cube: The amount of space occupied by a cube, calculated as the side length cubed (Side³).

What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math

▶

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.

Fun Fact

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