![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
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 value of \( \frac{6}{\sqrt{5}-\sqrt{3}} \), it being given that \( \sqrt{3}=1.732 \) and \( \sqrt{5}=2.236 \).
Given:
\( \sqrt{3}=1.732 \) and \( \sqrt{5}=2.236 \).
To do:
We have to find the value of \( \frac{6}{\sqrt{5}-\sqrt{3}} \).
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,
$\frac{6}{\sqrt{5}-\sqrt{3}}=\frac{6(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}$
$=\frac{6(\sqrt{5}+\sqrt{3})}{(\sqrt{5})^{2}-(\sqrt{3})^{2}}$
$=\frac{6(\sqrt{5}+\sqrt{3})}{5-3}$
$=\frac{6(\sqrt{5}+\sqrt{3})}{2}$
$=3(\sqrt{5}+\sqrt{3})$
$=3[2.236+1.732]$
$=3(3.968)$
$=11.904$
The value of \( \frac{6}{\sqrt{5}-\sqrt{3}} \) is $11.904$.