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 sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of -2744.
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 multiplying a negative number by itself three times results in a negative number.
The cube of -2744 can be written as \((-2744)^3\), which is the exponential form.
Or it can also be written in arithmetic form as, \(-2744 \times -2744 \times -2744\).
To verify whether a number is a cube number, we can use the following three methods: the multiplication method, a factor formula (\(a^3\)), or by using a calculator. These methods will help compute the cube of numbers faster and easier without confusion or errors during evaluation.
The multiplication method is a process in mathematics used to find the product of numbers 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. \((-2744)^3 = -2744 \times -2744 \times -2744\)
Step 2: The answer is -20,582,542,016. Hence, the cube of -2744 is -20,582,542,016.
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 -2744 into two parts, as \(a\) and \(b\). Let \(a = -2700\) and \(b = -44\), so \(a + b = -2744\)
Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\)
Step 3: Calculate each term \(a^3 = (-2700)^3\) \(3a^2b = 3 \times (-2700)^2 \times (-44)\) \(3ab^2 = 3 \times (-2700) \times (-44)^2\) \(b^3 = (-44)^3\)
Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((-2700 + -44)^3 = (-2700)^3 + 3 \times (-2700)^2 \times (-44) + 3 \times (-2700) \times (-44)^2 + (-44)^3\) \((-2744)^3 = -19,683,000,000 + 10,594,560,000 + 15,830,400 + -85,184\) \((-2744)^3 = -20,582,542,016\)
Step 5: Hence, the cube of -2744 is -20,582,542,016.
To find the cube of -2744 using a calculator, input the number -2744 and use the cube function (if available) or multiply \(-2744 \times -2744 \times -2744\). This operation calculates the value of \((-2744)^3\), resulting in -20,582,542,016. It’s a quick way to determine the cube without manual computation.
Step 1: Ensure the calculator is functioning properly.
Step 2: Input -2744.
Step 3: If the calculator has a cube function, press it to calculate \((-2744)^3\).
Step 4: If there is no cube function on the calculator, simply multiply -2744 three times manually.
Step 5: The calculator will display -20,582,542,016.
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 happen:
What is the cube and cube root of -2744?
The cube of -2744 is -20,582,542,016 and the cube root of -2744 is -14.
First, let’s find the cube of -2744.
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 \((-2744)^3 = -20,582,542,016\)
Next, we must find the cube root of -2744
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 \(\sqrt[3]{-2744} = -14\)
Hence the cube of -2744 is -20,582,542,016 and the cube root of -2744 is -14.
If the side length of the cube is -2744 cm, what is the volume?
The volume is -20,582,542,016 cm³.
Use the volume formula for a cube \(V = \text{Side}^3\).
Substitute -2744 for the side length: \(V = (-2744)^3 = -20,582,542,016 \text{ cm}^3\).
How much larger is \((-2744)^3\) than \((-2000)^3\)?
\((-2744)^3 - (-2000)^3 = -19,582,542,016\).
First find the cube of \((-2744)^3\), which is -20,582,542,016.
Next, find the cube of \((-2000)^3\), which is -8,000,000,000.
Now, find the difference between them using the subtraction method. \(-20,582,542,016 - (-8,000,000,000) = -12,582,542,016\)
Therefore, \((-2744)^3\) is -12,582,542,016 larger than \((-2000)^3\).
If a cube with a side length of -2744 cm is compared to a cube with a side length of -1000 cm, how much larger is the volume of the first cube?
The volume of the cube with a side length of -2744 cm is -20,582,542,016 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).
Cubing -2744 means multiplying -2744 by itself three times: \(-2744 \times -2744 = 7,529,536\), and then \(7,529,536 \times -2744 = -20,582,542,016\).
The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube.
Therefore, the volume of the cube is -20,582,542,016 cm³.
Estimate the cube of -2740 using the cube of -2744.
The cube of -2740 is approximately -20,582,542,016.
First, identify the cube of -2744,
The cube of -2744 is \((-2744)^3 = -20,582,542,016\).
Since -2740 is only a tiny bit more than -2744, the cube of -2740 will be almost the same as the cube of -2744.
The cube of -2740 is approximately -20,582,542,016 because the difference between -2740 and -2744 is very small.
So, we can approximate the value as -20,582,542,016.
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.