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{30}{5 \sqrt{3}-3 \sqrt{5}} $
Given:
\( \frac{30}{5 \sqrt{3}-3 \sqrt{5}} \)
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,
$\frac{30}{5 \sqrt{3}-3 \sqrt{5}}=\frac{30(5 \sqrt{3}+3 \sqrt{5})}{(5 \sqrt{3}-3 \sqrt{5})(5 \sqrt{3}+3 \sqrt{5})}$
$=\frac{30(5 \sqrt{3}+3 \sqrt{5})}{(5 \sqrt{3})^{2}-(3 \sqrt{5})^{2}}$
$=\frac{30(5 \sqrt{3}+3 \sqrt{5})}{25 \times 3-9 \times 5}$
$=\frac{30(5 \sqrt{3}+3 \sqrt{5})}{75-45}$
$=\frac{30(5 \sqrt{3}+3 \sqrt{5})}{30}$
$=5 \sqrt{3}+3 \sqrt{5}$
Hence, $\frac{30}{5 \sqrt{3}-3 \sqrt{5}}=5 \sqrt{3}+3 \sqrt{5}$.
32 Views
