- 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
Express each one of the following with rational denominator:$ \frac{1}{\sqrt{6}-\sqrt{5}} $
Given:
\( \frac{1}{\sqrt{6}-\sqrt{5}} \)
To do:
We have to express the given fraction with rational denominator.
Solution:
We know that,
Rationalising factor of a fraction with denominator ${\sqrt{a}}$ is ${\sqrt{a}}$.
Rationalising factor of a fraction with denominator ${\sqrt{a}-\sqrt{b}}$ is ${\sqrt{a}+\sqrt{b}}$.
Rationalising factor of a fraction with denominator ${\sqrt{a}+\sqrt{b}}$ is ${\sqrt{a}-\sqrt{b}}$.
Therefore,
$\frac{1}{\sqrt{6}-\sqrt{5}}=\frac{1(\sqrt{6}+\sqrt{5})}{(\sqrt{6}-\sqrt{5})(\sqrt{6}+\sqrt{5})}$
$=\frac{\sqrt{6}+\sqrt{5}}{(\sqrt{6})^{2}-(\sqrt{5})^{2}}$ [Since $(a+b)(a-b)=a^{2}-b^{2}$]
$=\frac{\sqrt{6}+\sqrt{5}}{6-5}$
$=\frac{\sqrt{6}+\sqrt{5}}{1}$
$=\sqrt{6}+\sqrt{5}$
Hence, $\frac{1}{\sqrt{6}-\sqrt{5}}=\sqrt{6}+\sqrt{5}$.
To Continue Learning Please Login
Login with Google