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 -25.
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 -25 can be written as (-25)³, which is the exponential form. Or it can also be written in arithmetic form as, -25 × -25 × -25.
To determine whether a number is a cube number, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These methods help in cubing numbers faster and easier without confusion or errors 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. (-25)³ = -25 × -25 × -25 Step 2: You get -15,625 as the answer. Hence, the cube of -25 is -15,625.
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 -25 into two parts, such as -20 and -5. Let a = -20 and b = -5, so a + b = -25 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = (-20)³ 3a²b = 3 × (-20)² × (-5) 3ab² = 3 × (-20) × (-5)² b³ = (-5)³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (-20 + -5)³ = (-20)³ + 3 × (-20)² × (-5) + 3 × (-20) × (-5)² + (-5)³ (-25)³ = -8000 + 6000 + 1500 - 125 (-25)³ = -15,625 Step 5: Hence, the cube of -25 is -15,625.
To find the cube of -25 using a calculator, input the number -25 and use the cube function (if available) or multiply -25 × -25 × -25. This operation calculates the value of (-25)³, resulting in -15,625. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press the negative sign followed by 2 and 5 Step 3: If the calculator has a cube function, press it to calculate (-25)³. Step 4: If there is no cube function on the calculator, simply multiply -25 three times manually. Step 5: The calculator will display -15,625.
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 might occur during the process of cubing a number. Let us take a look at five of the major mistakes to avoid:
What is the cube and cube root of -25?
The cube of -25 is -15,625 and the cube root of -25 is approximately -2.924.
First, let’s find the cube of -25. 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 (-25)³ = -15,625. Next, we must find the cube root of -25. 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 ∛(-25) ≈ -2.924. Hence the cube of -25 is -15,625 and the cube root of -25 is approximately -2.924.
If the side length of a cube is -25 cm, what is the volume?
The volume is -15,625 cm³.
Use the volume formula for a cube V = Side³. Substitute -25 for the side length: V = (-25)³ = -15,625 cm³.
How much larger is (-25)³ than (-20)³?
(-25)³ – (-20)³ = -7,625.
First, find the cube of (-25), which is -15,625. Next, find the cube of (-20), which is -8,000. Now, find the difference between them using the subtraction method. -15,625 – (-8,000) = -7,625. Therefore, (-25)³ is -7,625 larger than (-20)³.
If a cube with a side length of -25 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 -25 cm is -15,625 cm³.
To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing -25 means multiplying -25 by itself three times: -25 × -25 = 625, and then 625 × -25 = -15,625. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is -15,625 cm³.
Estimate the cube of -24.9 using the cube of -25.
The cube of -24.9 is approximately -15,625.
First, identify the cube of -25. The cube of -25 is (-25)³ = -15,625. Since -24.9 is only a tiny bit more than -25, the cube of -24.9 will be almost the same as the cube of -25. The cube of -24.9 is approximately -15,625 because the difference between -24.9 and -25 is very small. So, we can approximate the value as -15,625.
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, 2³ represents 2 × 2 × 2 equals 8. Perfect Cube: A number that can be expressed as the cube of an integer. For example, 8 is a perfect cube because it is 2³. Cube Root: The number 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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