Prove that if n is a natural number and if n has a rational square root then in fact the square root of n is an integer
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
140949
Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
121469
Proof of observations on natural numbers being expressed as differences of squares.
121694
How to prove $\log n \leq \sqrt n$ over natural numbers?
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
41486
If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
87764
Prove that the difference between two rational numbers is rational
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
101162
Square root of $2$ is irrational
30478
How to prove that a number is irrational
123427
Proving the sum of the first $n$ natural numbers by induction
24301
Can a finite sum of square roots be an integer?
23752
Proving Irrationality
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
16660
Prove that any positive number has an $n$th root