Rationalise the denominator in the following expression:
$\frac{1}{\sqrt{5}-\sqrt{3}}$
$\frac{1}{\sqrt{5}-\sqrt{3}}$
(A) To rationalise the denominator,multiply the numerator and the denominator by the conjugate of the denominator,which is $(\sqrt{5} + \sqrt{3})$.
$\frac{1}{\sqrt{5}-\sqrt{3}} \times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}$
$= \frac{\sqrt{5}+\sqrt{3}}{(\sqrt{5})^2 - (\sqrt{3})^2}$
$= \frac{\sqrt{5}+\sqrt{3}}{5 - 3}$
$= \frac{\sqrt{5}+\sqrt{3}}{2}$
$\frac{1}{\sqrt{5}-\sqrt{3}} \times \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}$
$= \frac{\sqrt{5}+\sqrt{3}}{(\sqrt{5})^2 - (\sqrt{3})^2}$
$= \frac{\sqrt{5}+\sqrt{3}}{5 - 3}$
$= \frac{\sqrt{5}+\sqrt{3}}{2}$
Explore More
Similar Questions
For each question,select the proper option from four options given,to make the statement true: $(5^{-2})^{3} = \ldots \ldots \ldots$
Easy
View SolutionIf $2^{x-2} \cdot 3^{2x-6} = 36$,then find $x$.
Medium
View SolutionSimplify: $(3 \sqrt{5}-5 \sqrt{2})(4 \sqrt{5}+3 \sqrt{2})$
Difficult
View SolutionFill in the blanks to make the following statement true:
$\sqrt{1 \frac{25}{144}} = \ldots$
$\sqrt{1 \frac{25}{144}} = \ldots$
Easy
View SolutionFind the value of $(625)^{-\frac{3}{4}}$.
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo