Last updated on May 26th, 2025
When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 476.
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 multiplied by itself three times results in a negative number. The cube of 476 can be written as \(476^3\), which is the exponential form. Or it can also be written in arithmetic form as, \(476 \times 476 \times 476\).
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 (\(a^3\)), 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. By Multiplication Method Using a Formula Using a Calculator
The multiplication method is a process in mathematics used to find the product of 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. \(476^3 = 476 \times 476 \times 476\) Step 2: You get 107,503,936 as the answer. Hence, the cube of 476 is 107,503,936.
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 476 into two parts, such as 400 and 76. Let \(a = 400\) and \(b = 76\), so \(a + b = 476\). Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\). Step 3: Calculate each term \(a^3 = 400^3\) \(3a^2b = 3 \times 400^2 \times 76\) \(3ab^2 = 3 \times 400 \times 76^2\) \(b^3 = 76^3\) Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((400 + 76)^3 = 400^3 + 3 \times 400^2 \times 76 + 3 \times 400 \times 76^2 + 76^3\) \(476^3 = 64,000,000 + 36,480,000 + 6,912,000 + 111,936\) \(476^3 = 107,503,936\) Step 5: Hence, the cube of 476 is 107,503,936.
To find the cube of 476 using a calculator, input the number 476 and use the cube function (if available) or multiply \(476 \times 476 \times 476\). This operation calculates the value of \(476^3\), resulting in 107,503,936. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input 476. Step 3: If the calculator has a cube function, press it to calculate \(476^3\). Step 4: If there is no cube function on the calculator, simply multiply 476 three times manually. Step 5: The calculator will display 107,503,936.
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 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 476?
The cube of 476 is 107,503,936 and the cube root of 476 is approximately 7.798.
First, let’s find the cube of 476. We know that the cube of a number is \(x^3 = y\), where \(x\) is the given number, and \(y\) is the cubed value of that number. So, we get \(476^3 = 107,503,936\). Next, we must find the cube root of 476. 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 \(\sqrt[3]{476} \approx 7.798\). Hence, the cube of 476 is 107,503,936, and the cube root of 476 is approximately 7.798.
If the side length of the cube is 476 cm, what is the volume?
The volume is 107,503,936 cm\(^3\).
Use the volume formula for a cube \(V = \text{Side}^3\). Substitute 476 for the side length: \(V = 476^3 = 107,503,936\) cm\(^3\).
How much larger is \(476^3\) than \(400^3\)?
\(476^3 - 400^3 = 43,503,936\).
First, find the cube of \(476^3\), which is 107,503,936. Next, find the cube of \(400^3\), which is 64,000,000. Now, find the difference between them using the subtraction method. 107,503,936 - 64,000,000 = 43,503,936. Therefore, \(476^3\) is 43,503,936 larger than \(400^3\).
If a cube with a side length of 476 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 476 cm is 107,503,936 cm\(^3\).
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 476 means multiplying 476 by itself three times: 476 \(\times\) 476 = 226,576, and 226,576 \(\times\) 476 = 107,503,936. 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 107,503,936 cm\(^3\).
Estimate the cube of 475.9 using the cube of 476.
The cube of 475.9 is approximately 107,503,936.
First, identify the cube of 476, The cube of 476 is \(476^3 = 107,503,936\). Since 475.9 is only a tiny bit less than 476, the cube of 475.9 will be almost the same as the cube of 476. The cube of 475.9 is approximately 107,503,936 because the difference between 475.9 and 476 is very small. So, we can approximate the value as 107,503,936.
Binomial Formula: It is 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: It is 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 \(2 \times 2 \times 2 = 8\). Perfect Cube: A number that can be expressed as the cube of an integer. Volume of a Cube: The amount of space occupied by a cube, calculated as the side length cubed.
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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