# Is this proposition <msqrt> 2

Is this proposition $\sqrt{2}$ + $\sqrt{3}$ is an irrational number." true or false?
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jugf5
If it were rational, its square would also be rational, so $2+3+2\sqrt{6}$ would be rational and hence $\sqrt{6}$ would be rational.
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therightwomanwf
$\sqrt{2}+\sqrt{3}=\frac{p}{q}\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}2={\left(\frac{p}{q}-\sqrt{3}\right)}^{2}\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}\frac{3+\frac{{p}^{2}}{{q}^{2}}-2}{2\frac{p}{q}}=\sqrt{3}$