102 LearnersLast updated on May 26th, 2025
Cube of -64
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 -64.
Cube of -64
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 -64 can be written as (-64)^3, which is the exponential form. Or it can also be written in arithmetic form as, -64 × -64 × -64.
How to Calculate the Value of Cube of -64
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 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
By Multiplication Method
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. (-64)^3 = -64 × -64 × -64 Step 2: You get -262,144 as the answer. Hence, the cube of -64 is -262,144.
Using a Formula (a^3)
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 -64 into two parts, as -60 and -4. Let a = -60 and b = -4, so a + b = -64 Step 2: Now, apply the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Step 3: Calculate each term a^3 = (-60)^3 3a^2b = 3 × (-60)^2 × (-4) 3ab^2 = 3 × (-60) × (-4)^2 b^3 = (-4)^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-60 - 4)^3 = (-60)^3 + 3 × (-60)^2 × (-4) + 3 × (-60) × (-4)^2 + (-4)^3 (-64)^3 = -216,000 - 43,200 - 2,880 - 64 (-64)^3 = -262,144 Step 5: Hence, the cube of -64 is -262,144.
Using a Calculator
To find the cube of -64 using a calculator, input the number -64 and use the cube function (if available) or multiply -64 × -64 × -64. This operation calculates the value of (-64)^3, resulting in -262,144. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input -64 Step 3: If the calculator has a cube function, press it to calculate (-64)^3. Step 4: If there is no cube function on the calculator, simply multiply -64 three times manually. Step 5: The calculator will display -262,144.
Tips and Tricks for the Cube of -64
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.
Common Mistakes to Avoid When Calculating the Cube of -64
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:
Mistake 1
Incorrect Multiplication
Some might multiply the numbers only twice, like -64 × -64 and not -64 × -64 × -64. Always remember that (-64)^3 = -64 × -64 × -64.
Solved Examples on Cube of -64
Problem 1
What is the cube and cube root of -64?
The cube of -64 is -262,144 and the cube root of -64 is -4.
Explanation
First, let’s find the cube of -64. 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 (-64)^3 = -262,144 Next, we must find the cube root of -64 We know that the cube root of a number ‘x’, such that ∛x = y Where ‘x’ is the given number, and y is the cube root value of the number So, we get ∛(-64) = -4 Hence the cube of -64 is -262,144 and the cube root of -64 is -4.
Problem 2
If the side length of a cube is -64 cm, what is the volume?
The volume is -262,144 cm³.
Explanation
Use the volume formula for a cube V = Side^3. Substitute -64 for the side length: V = (-64)^3 = -262,144 cm³.
Problem 3
How much smaller is (-64)^3 than (-60)^3?
(-64)^3 - (-60)^3 = -46,144.
Explanation
First find the cube of (-64)^3, that is -262,144 Next, find the cube of (-60)^3, which is -216,000 Now, find the difference between them using the subtraction method. -262,144 - (-216,000) = -46,144 Therefore, (-64)^3 is 46,144 smaller than (-60)^3.
Problem 4
If a cube with a side length of -64 cm is compared to a cube with a side length of -4 cm, how much smaller is the volume of the smaller cube?
The volume of the cube with a side length of -64 cm is -262,144 cm³ and the volume of the cube with a side length of -4 cm is -64 cm³. The smaller cube's volume is -64 cm³ smaller.
Explanation
To find the volume of a cube, multiply the side length by itself three times. Cubing -64 means multiplying -64 by itself three times: -64 × -64 = 4,096, and then 4,096 × -64 = -262,144 cm³. For the smaller cube, cubing -4 means multiplying -4 by itself three times: -4 × -4 = 16, and then 16 × -4 = -64 cm³. The difference in volume is -262,144 cm³ - (-64 cm³) = -262,080 cm³.
Problem 5
Estimate the cube of -63.9 using the cube of -64.
The cube of -63.9 is approximately -262,144.
Explanation
First, identify the cube of -64, The cube of -64 is (-64)^3 = -262,144. Since -63.9 is only a tiny bit more than -64, the cube of -63.9 will be almost the same as the cube of -64. The cube of -63.9 is approximately -262,144 because the difference between -63.9 and -64 is very small. So, we can approximate the value as -262,144.
FAQs on Cube of -64
1.What are the perfect cubes up to -64?
2.How do you calculate (-64)^3?
3.What is the meaning of (-64)^3?
4.What is the cube root of -64?
5.Is -64 a perfect cube?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Cube of -64?
8.How do technology and digital tools in United States support learning Algebra and Cube of -64?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Cube of -64
1. 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. 2. Cube of a Number: Multiplying a number by itself three times is called the cube of a number. 3. 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 × 2 × 2 equals 8. 4. Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself three times. 5. Cube Root: The number that, when multiplied by itself three times, gives the original number. For example, the cube root of -64 is -4.
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Jaskaran Singh Saluja
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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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