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 when comparing the sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 691.
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 691 can be written as 691³, which is the exponential form. Or it can also be written in arithmetic form as, 691 × 691 × 691.
In order to check whether a number is a cube number or not, we can use the following three methods: 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. 691³ = 691 × 691 × 691
Step 2: You get 330,761,771 as the answer. Hence, the cube of 691 is 330,761,771.
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 691 into two parts. Let a = 690 and b = 1, so a + b = 691
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term
a³ = 690³
3a²b = 3 × 690² × 1
3ab² = 3 × 690 × 1²
b³ = 1³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(690 + 1)³ = 690³ + 3 × 690² × 1 + 3 × 690 × 1² + 1³
691³ = 328,509,000 + 1,428,300 + 2,070 + 1
691³ = 330,761,771
Step 5: Hence, the cube of 691 is 330,761,771.
To find the cube of 691 using a calculator, input the number 691 and use the cube function (if available) or multiply 691 × 691 × 691. This operation calculates the value of 691³, resulting in 330,761,771. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Press 6, 9, followed by 1
Step 3: If the calculator has a cube function, press it to calculate 691³.
Step 4: If there is no cube function on the calculator, simply multiply 691 three times manually.
Step 5: The calculator will display 330,761,771.
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 691?
The cube of 691 is 330,761,771 and the cube root of 691 is approximately 8.844.
First, let’s find the cube of 691.
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 691³ = 330,761,771
Next, we must find the cube root of 691 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 ∛691 ≈ 8.844
Hence, the cube of 691 is 330,761,771 and the cube root of 691 is approximately 8.844.
If the side length of a cube is 691 cm, what is the volume?
The volume is 330,761,771 cm³.
Use the volume formula for a cube V = Side³.
Substitute 691 for the side length: V = 691³ = 330,761,771 cm³.
How much larger is 691³ than 490³?
691³ – 490³ = 328,652,621.
First, find the cube of 691, which is 330,761,771.
Next, find the cube of 490, which is 2,109,150.
Now, find the difference between them using the subtraction method.
330,761,771 – 2,109,150 = 328,652,621
Therefore, 691³ is 328,652,621 larger than 490³.
If a cube with a side length of 691 cm is compared to a cube with a side length of 10 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 691 cm is 330,761,771 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 691 means multiplying 691 by itself three times: 691 × 691 = 477,481, and then 477,481 × 691 = 330,761,771.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 330,761,771 cm³.
Estimate the cube 690.9 using the cube 691.
The cube of 690.9 is approximately 330,761,771.
First, identify the cube of 691.
The cube of 691 is 691³ = 330,761,771.
Since 690.9 is only a tiny bit less than 691, the cube of 690.9 will be almost the same as the cube of 691.
The cube of 690.9 is approximately 330,761,771 because the difference between 690.9 and 691 is very small.
So, we can approximate the value as 330,761,771.
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.