A perfect cube is a number multiplied by itself three times. In other words, it is the third exponent of any natural number. So, if a is the perfect cube of b, then mathematically it can be expressed as a = b3. Some examples of perfect cubes are 1, 8, 27, 64, 125, etc. When we multiply a natural number three times by itself, we get a perfect cube. For example, 2×2×2=8, which is a perfect cube of number 2. All natural numbers are not perfect cubes. Why? Let's find out in this article!
Given below is the list of perfect cubes of the first 10 natural numbers:
|Number||Cube of the number|
|2||2×2×2 = 8|
|3||3×3×3 = 27|
|4||4×4×4 = 64|
|5||5×5×5 = 125|
|6||6×6×6 = 216|
|7||7×7×7 = 343|
|8||8×8×8 = 512|
|9||9×9×9 = 729|
|10||10×10×10 = 1000|
Perfect cubes can be found by multiplying a number three times by itself. For example, to find the perfect cube of 25, we need to multiply 25 three times as, 25×25×25 = 625×25 = 15625. To find out whether a number is a perfect cube or not, we need to find the cube root of the number. If the answer results in a natural number, then the given number is considered a perfect cube. If the cube root of the given number is not a natural number, then it is not considered a perfect cube.
Solved Examples on Perfect Cubes
Example 1: Find the perfect cube of 13.
Solution: The perfect cube of 13 is 13×13×13, which is 169×13 = 2197. Therefore, the perfect cube of 13 is 2197.
FAQs on Perfect Cubes
What are the First 20 Perfect Cubes?
The first 20 perfect cubes can be calculated by finding the third exponent of the first 20 natural numbers. The list of the first 20 perfect cubes includes 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, and 8000.
How do You Find a Perfect Cube of a Number?
A perfect cube of a number can be found by multiplying the numbers three times to itself. For example, the perfect cube of 4 is 4×4×4, which is 64.