- 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
Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.
Given :
The given number is 3645.
To do :
We have to find the smallest number by which 3645 must be divided so that it becomes a perfect square and also the square root of the number so obtained.
Solution :
Prime factorisation of 3645,
$3645=3\times3\times3\times3\times3\times3\times5$
$= 3^2 \times3^2\times3^2\times5$
To get a perfect square, we have to divide the factors by 5.
So, $3^2 \times 3^2 \times 3^2\times5\div5= 3^2 \times 3^2\times3^2\times1 $
$= (3 \times3\times3)^2 $
$= (27)^2$
$=729$
$\sqrt{729} = \sqrt{(27)^2}$
$= 27$
Therefore, 729 has to be divided by 5 to get a perfect square.
The square root of 729 is 27.
Advertisements