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
Rationalise the denominator and simplify:$ \frac{2 \sqrt{3}-\sqrt{5}}{2 \sqrt{2}+3 \sqrt{3}} $
Given:
\( \frac{2 \sqrt{3}-\sqrt{5}}{2 \sqrt{2}+3 \sqrt{3}} \)
To do:
We have to rationalise the denominator and simplify the given expression.
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,
$\frac{2 \sqrt{3}-\sqrt{5}}{2 \sqrt{2}+3 \sqrt{3}}=\frac{(2 \sqrt{3}-\sqrt{5})(2 \sqrt{2}-3 \sqrt{3})}{(2 \sqrt{2}+3 \sqrt{3})(2 \sqrt{2}-3 \sqrt{3})}$
$=\frac{4 \sqrt{6}-6 \sqrt{3} \times \sqrt{3}-2 \sqrt{10}+3 \sqrt{15}}{(2 \sqrt{2})^{2}-(3 \sqrt{3})^{2}}$
$=\frac{4 \sqrt{6}-18-2 \sqrt{10}+3 \sqrt{15}}{8-27}$
$=\frac{-18-2 \sqrt{10}+4 \sqrt{6}+3 \sqrt{15}}{-19}$
$=\frac{18+2 \sqrt{10}-4 \sqrt{6}-3 \sqrt{15}}{19}$
Hence, $\frac{2 \sqrt{3}-\sqrt{5}}{2 \sqrt{2}+3 \sqrt{3}}=\frac{18+2 \sqrt{10}-4 \sqrt{6}-3 \sqrt{15}}{19}$.
88 Views
