Last updated on June 2nd, 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 the cube of 631.
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 631 can be written as \(631^3\), which is the exponential form. Or it can also be written in arithmetic form as, 631 × 631 × 631.
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 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. \(631^3 = 631 \times 631 \times 631\) Step 2: Calculate to get 251,537,791 as the answer. Hence, the cube of 631 is 251,537,791.
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 631 into two parts, such as \(a\) and \(b\). Let \(a = 600\) and \(b = 31\), so \(a + b = 631\) Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) Step 3: Calculate each term \(a^3 = 600^3\) \(3a^2b = 3 \times 600^2 \times 31\) \(3ab^2 = 3 \times 600 \times 31^2\) \(b^3 = 31^3\) Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((600 + 31)^3 = 600^3 + 3 \times 600^2 \times 31 + 3 \times 600 \times 31^2 + 31^3\) \(631^3 = 216,000,000 + 33,480,000 + 1,728,600 + 29,791\) \(631^3 = 251,537,791\) Step 5: Hence, the cube of 631 is 251,537,791.
To find the cube of 631 using a calculator, input the number 631 and use the cube function (if available) or multiply 631 × 631 × 631. This operation calculates the value of \(631^3\), resulting in 251,537,791. 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 3 and 1. Step 3: If the calculator has a cube function, press it to calculate \(631^3\). Step 4: If there is no cube function on the calculator, simply multiply 631 three times manually. Step 5: The calculator will display 251,537,791.
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.
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:
What is the cube and cube root of 631?
The cube of 631 is 251,537,791 and the cube root of 631 is approximately 8.574.
First, let’s find the cube of 631. We know that the cube of a number, such that \(x^3 = y\), where \(x\) is the given number, and \(y\) is the cubed value of that number. So, we get \(631^3 = 251,537,791\). Next, we must find the cube root of 631. We know that the cube root of a number \(x\), 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 \(\sqrt[3]{631} \approx 8.574\). Hence, the cube of 631 is 251,537,791 and the cube root of 631 is approximately 8.574.
If the side length of a cube is 631 cm, what is the volume?
The volume is 251,537,791 cm\(^3\).
Use the volume formula for a cube \(V = \text{Side}^3\). Substitute 631 for the side length: \(V = 631^3 = 251,537,791\) cm\(^3\).
How much larger is \(631^3\) than \(530^3\)?
\(631^3 - 530^3 = 145,529,791\).
First, find the cube of \(631^3\), which is 251,537,791. Next, find the cube of \(530^3\), which is 106,008,000. Now, find the difference between them using the subtraction method. 251,537,791 - 106,008,000 = 145,529,791. Therefore, \(631^3\) is 145,529,791 larger than \(530^3\).
If a cube with a side length of 631 cm is compared to a cube with a side length of 200 cm, how much larger is the volume of the larger cube?
The volume of the cube with a side length of 631 cm is 251,537,791 cm\(^3\).
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 631 means multiplying 631 by itself three times: 631 × 631 = 398,161, and then 398,161 × 631 = 251,537,791. 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 251,537,791 cm\(^3\).
Estimate the cube of 630.9 using the cube of 631.
The cube of 630.9 is approximately 251,537,791.
First, identify the cube of 631, The cube of 631 is \(631^3 = 251,537,791\). Since 630.9 is only a tiny bit less than 631, the cube of 630.9 will be almost the same as the cube of 631. The cube of 630.9 is approximately 251,537,791 because the difference between 630.9 and 631 is very small. So, we can approximate the value as 251,537,791.
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. Volume of a Cube: The amount of space inside a cube, calculated by cubing the side length. Cube Root: The number that, when multiplied by itself three times, gives the original number.
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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