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}{2 \sqrt{5}-\sqrt{3}} $
Given:
\( \frac{1}{2 \sqrt{5}-\sqrt{3}} \)
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,
$\frac{1}{2 \sqrt{5}-\sqrt{3}}=\frac{1 \times(2 \sqrt{5}+\sqrt{3})}{(2 \sqrt{5}-\sqrt{3})(2 \sqrt{5}+\sqrt{3})}$
$=\frac{2 \sqrt{5}+\sqrt{3}}{(2 \sqrt{5})^{2}-(\sqrt{3})^{2}}$ [Since $(a+b)(a-b)=a^2-b^2$]
$=\frac{2 \sqrt{5}+\sqrt{3}}{20-3}$
$=\frac{2 \sqrt{5}+\sqrt{3}}{17}$
Hence, $\frac{1}{2 \sqrt{5}-\sqrt{3}}=\frac{2 \sqrt{5}+\sqrt{3}}{17}$.
54 Views
