![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
Rationalise the denominators of each of the following:$ \frac{\sqrt{3}+1}{\sqrt{2}} $
Given:
\( \frac{\sqrt{3}+1}{\sqrt{2}} \)To do:
We have to rationalise the denominator of 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,
$\frac{\sqrt{3}+1}{\sqrt{2}}=\frac{(\sqrt{3}+1) \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}}$
$=\frac{\sqrt{3\times2}+1\times\sqrt{2}}{(\sqrt{2})^2}$
$=\frac{\sqrt{6}+\sqrt{2}}{2}$
Hence, $\frac{\sqrt{3}+1}{\sqrt{2}}=\frac{\sqrt{6}+\sqrt{2}}{2}$.
Advertisements