$\sqrt 2+ \sqrt{3} \approx 3.14$

Question

The square $$\sqrt 2+ \sqrt{3} \approx 3.14$$ Is this a coincidence or is their some mathemtical significance?

Answer 1

I think that this and this are fairly relevant here. It is the case that $\sqrt 2 + \sqrt 3 \approx 3.14 \approx \pi$, but it is not the case that $\sqrt 2 + \sqrt 3 = \pi$.

You are falling victim to the "strong law of small numbers".