Last updated on May 29th, 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 the cube of 585.
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 585 can be written as 585^3, which is the exponential form. Or it can also be written in arithmetic form as, \(585 \times 585 \times 585\).
To determine 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 individuals 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 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. \(585^3 = 585 \times 585 \times 585\) Step 2: You get 200,037,825 as the answer. Hence, the cube of 585 is 200,037,825.
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 585 into two parts. Let \(a = 580\) and \(b = 5\), so \(a + b = 585\). Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\). Step 3: Calculate each term: \(a^3 = 580^3\) \(3a^2b = 3 \times 580^2 \times 5\) \(3ab^2 = 3 \times 580 \times 5^2\) \(b^3 = 5^3\) Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((580 + 5)^3 = 580^3 + 3 \times 580^2 \times 5 + 3 \times 580 \times 5^2 + 5^3\) \(585^3 = 195,112,000 + 5,040,000 + 43,500 + 125\) \(585^3 = 200,037,625\) Step 5: Hence, the cube of 585 is 200,037,625.
To find the cube of 585 using a calculator, input the number 585 and use the cube function (if available) or multiply \(585 \times 585 \times 585\). This operation calculates the value of \(585^3\), resulting in 200,037,625. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press 5, 8, and 5. Step 3: If the calculator has a cube function, press it to calculate \(585^3\). Step 4: If there is no cube function on the calculator, simply multiply 585 three times manually. Step 5: The calculator will display 200,037,625.
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 individuals might make 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 585?
The cube of 585 is 200,037,625 and the cube root of 585 is approximately 8.393.
First, let’s find the cube of 585. 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 \(585^3 = 200,037,625\). Next, we must find the cube root of 585. 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 \(\sqrt[3]{585} \approx 8.393\). Hence, the cube of 585 is 200,037,625 and the cube root of 585 is approximately 8.393.
If the side length of the cube is 585 cm, what is the volume?
The volume is 200,037,625 cm³.
Use the volume formula for a cube \(V = \text{Side}^3\). Substitute 585 for the side length: \(V = 585^3 = 200,037,625\) cm³.
How much larger is \(585^3\) than \(480^3\)?
\(585^3 - 480^3 = 129,297,985\).
First, find the cube of \(585^3\), which is 200,037,625. Next, find the cube of \(480^3\), which is 70,739,640. Now, find the difference between them using the subtraction method. 200,037,625 - 70,739,640 = 129,297,985. Therefore, \(585^3\) is 129,297,985 larger than \(480^3\).
If a cube with a side length of 585 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 585 cm is 200,037,625 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 585 means multiplying 585 by itself three times: 585 × 585 = 342,225, and then 342,225 × 585 = 200,037,625. The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube. Therefore, the volume of the cube is 200,037,625 cm³.
Estimate the cube 584.9 using the cube 585.
The cube of 584.9 is approximately 200,037,625.
First, identify the cube of 585, The cube of 585 is \(585^3 = 200,037,625\). Since 584.9 is only slightly less than 585, the cube of 584.9 will be almost the same as the cube of 585. The cube of 584.9 is approximately 200,037,625 because the difference between 584.9 and 585 is very small. So, we can approximate the value as 200,037,625.
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. Perfect Cube: A number that can be expressed as the cube of an integer. For example, 27 is a perfect cube because it is \(3 \times 3 \times 3\). Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3.
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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