- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Write the cubes of 5 natural numbers of which are multiples of 7 and verify the following:
‘The cube of a multiple of 7 is a multiple of $7^3$′.
Given:
The cube of a multiple of 7 is a multiple of $7^3$
To do:
We have to write the cubes of 5 natural numbers of which are multiples of 7 and verify the given statement.
Solution:  
First 5 natural numbers which are multiple of 7 are 7, 14, 21, 28, 35.
Therefore,
$(7)^3=7\times7\times7=343$
$(14)^3=(2\times7)^3=2^3\times7^3$
$(21)^3=(3\times7)^3=3^3\times7^3$
$(28)^3=(4\times7)^3=4^3\times7^3$
$(35)^3=(5\times7)^3=5^3\times7^3$
Any number multiplied by $7^3$ is a multiple of it.
Therefore,
$7^3, 14^3, 21^3, 28^3, 35^3$ are all of multiples of $7^3$
Hence, the given statement is true. 
Advertisements