Rationalise the denominator in each of the following:
$\frac{5-2 \sqrt{6}}{5+2 \sqrt{6}}$

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(A) To rationalise the denominator,multiply the numerator and the denominator by the conjugate of the denominator,which is $(5-2 \sqrt{6})$.
$\frac{5-2 \sqrt{6}}{5+2 \sqrt{6}} \times \frac{5-2 \sqrt{6}}{5-2 \sqrt{6}}$
$= \frac{(5-2 \sqrt{6})^2}{(5)^2 - (2 \sqrt{6})^2}$
$= \frac{5^2 - 2(5)(2 \sqrt{6}) + (2 \sqrt{6})^2}{25 - (4 \times 6)}$
$= \frac{25 - 20 \sqrt{6} + 24}{25 - 24}$
$= \frac{49 - 20 \sqrt{6}}{1}$
$= 49 - 20 \sqrt{6}$

Explore More

Similar Questions

Rationalise the denominator of the following:
$\frac{3+\sqrt{2}}{4 \sqrt{2}}$

Difficult
View Solution

Represent $\sqrt{5}$ on the number line.

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.00323232 \ldots$

Difficult
View Solution

Show that $0.142857142857... = 0.\overline{142857} = \frac{1}{7}$.

Every rational number is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo