Show that


Show that $5-2 \sqrt{3}$ is an irrational number.


Let us assume that $5-2 \sqrt{3}$ is rational .Then, there exist positive co primes $a$ and $b$ such that

$5-2 \sqrt{3}=\frac{a}{b}$

$2 \sqrt{3}=\frac{a}{b}-5$


$\sqrt{3}=\frac{a-5 b}{2 b}$

This contradicts the fact that $\sqrt{3}$ is an irrational number

Hence $5-2 \sqrt{3}$ is irrational

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now