# Tagged Questions

Questions about real numbers not expressible as the quotient of two integers. For questions on determining whether a number is irrational, use the (rationality-testing) tag instead.

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### proving $\sqrt 2 + \sqrt 3$ is irrational [duplicate]

I need to proof that $\sqrt{3} + \sqrt{2}$ is irrational, without using the fact that an irrational number plus a rational number equals irrational. also, i can't use the rational root theorem. that's ...
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### If $x$ is an irrational number, then $3x^2 + 2$ is an irrational number? [closed]

Prove or disprove using direct or indirect proof that if $x$ is irrational, then $3x^2 + 2$ is irrational? Thank you in advance.
### Is $\pi^0$ actually rational? How about $\pi^i$? [duplicate]
Is there a rational argument that a transcendental or irrational number raised to zero should magically turn it into an integer, beyond obtuse convention? How about $\pi^i$? Is there a reasonable ...
### Alternative prrof of $\sqrt 2$ (and $\sqrt {\text {of any non square integer}}$ ) not being rational
Long time ago for an assignment, I submitted an alternative proof of $\sqrt 2$ not being rational along the following lines: suppose $\frac{a^2}{b^2}=2$ then we must also have $a=b+n$ for $a,b,n$ ...