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 61.
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 61 can be written as 61³, which is the exponential form. Or it can also be written in arithmetic form as, 61 × 61 × 61.
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 (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.
61³ = 61 × 61 × 61
Step 2: You get 226,981 as the answer.
Hence, the cube of 61 is 226,981.
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 61 into two parts.
Let a = 60 and b = 1, so a + b = 61
Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³
Step 3: Calculate each term a³ = 60³ , 3a²b = 3 × 60² × 1 , 3ab² = 3 × 60 × 1² , b³ = 1³
Step 4: Add all the terms together:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(60 + 1)³ = 60³ + 3 × 60² × 1 + 3 × 60 × 1² + 1³
61³ = 216,000 + 10,800 + 180 + 1 61³
= 226,981
Step 5: Hence, the cube of 61 is 226,981.
To find the cube of 61 using a calculator, input the number 61 and use the cube function (if available) or multiply 61 × 61 × 61. This operation calculates the value of 61³, resulting in 226,981. 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 1
Step 3: If the calculator has a cube function, press it to calculate 61³.
Step 4: If there is no cube function on the calculator, simply multiply 61 three times manually.
Step 5: The calculator will display 226,981.
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 61?
The cube of 61 is 226,981 and the cube root of 61 is approximately 3.914.
First, let’s find the cube of 61.
We know that the cube of a number is such that x³ = y, where x is the given number, and y is the cubed value of that number.
So, we get 61³ = 226,981.
Next, we must find the cube root of 61.
We know that the cube root of a number ‘x’ is such that ∛x = y, where ‘x’ is the given number, and y is the cube root value of the number.
So, we get ∛61 ≈ 3.914.
Hence, the cube of 61 is 226,981 and the cube root of 61 is approximately 3.914.
If the side length of the cube is 61 cm, what is the volume?
The volume is 226,981 cm³.
Use the volume formula for a cube V = Side³.
Substitute 61 for the side length: V = 61³ = 226,981 cm³.
How much larger is 61³ than 31³?
61³ – 31³ = 214,920.
First, find the cube of 61, which is 226,981.
Next, find the cube of 31, which is 29,791.
Now, find the difference between them using the subtraction method. 226,981 – 29,791 = 197,190.
Therefore, 61³ is 197,190 larger than 31³.
If a cube with a side length of 61 cm is compared to a cube with a side length of 1 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 61 cm is 226,981 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing 61 means multiplying 61 by itself three times: 61 × 61 = 3,721, and then 3,721 × 61 = 226,981.
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is 226,981 cm³.
Estimate the cube 60.1 using the cube 61.
The cube of 60.1 is approximately 226,981.
First, identify the cube of 61.
The cube of 61 is 61³ = 226,981.
Since 60.1 is only a tiny bit less than 61, the cube of 60.1 will be almost the same as the cube of 61.
The cube of 60.1 is approximately 226,981 because the difference between 60.1 and 61 is very small.
So, we can approximate the value as 226,981.
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.