Solved Examples on Perfect Cubes
Let’s solve some example problems on the concept of perfect cubes.
1. Determine if 64 is a perfect cube?
Solution:
64= 4×4×4= 43. So, 64 is a perfect cube.
2. Express 512 as a perfect cube?
Solution:
512= 8×8×8= 83. Hence, 512 is a perfect cube.
3. Determine the smallest perfect cube greater than 200?
Solution:
The cube root of 200 is approximately 6.3, and the next integer is 7. Therefore, 73 =343 is the smallest perfect cube greater than 200.
4. Find the difference between two consecutive perfect cubes that have a sum of 189?
Solution:
Let the consecutive perfect cubes be n3 and (n+1)3. According to the problem, n3 +(n+1)3=189.
Solving this equation, we find n=4. Therefore, the cubes are 43= 64 and 53= 125.
The difference between these cubes is 125−64= 61.
Perfect Cubes – Definition, List, Chart and Examples
Perfect cubes are numbers that result from multiplying an integer by itself twice. A number is said to be a perfect cube if it can be decomposed into a product of the same number thrice.
List of Perfect Cubes
Let’s discuss the definition and list of perfect cubes of numbers along with the stepwise method to find them.
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