Last updated on June 3rd, 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.
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.
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.
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.
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.
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.
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:
What is the cube and cube root of 690?
The cube of 690 is 328,509,000 and the cube root of 690 is approximately 8.879.
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.
If the side length of the cube is 690 cm, what is the volume?
The volume is 328,509,000 cm³.
Use the volume formula for a cube V = Side³.
Substitute 690 for the side length: V = 690³ = 328,509,000 cm³.
How much larger is 690³ than 400³?
690³ – 400³ = 292,909,000.
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.
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?
The volume of the cube with a side length of 690 cm is 328,509,000 cm³.
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.
Estimate the cube 689.9 using the cube 690.
The cube of 689.9 is approximately 328,509,000.
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.
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.
: He loves to play the quiz with kids through algebra to make kids love it.