Inequality involving exponential of square roots How can I show that:
$$ 2e^\sqrt{3} \leq 3e^\sqrt{2} $$
? (that's all I have)
Thank you so much!

Let $f(x)=\frac{e^{x}}{x^2}$. Then $$f'(x)=e^x\left(\frac{x-2}{x^3}\right)$$
So $f'(x)<0$ for $0<x<2$. Then $f(\sqrt{3})<f(\sqrt{2})$ and your result follows.
