Proof by contradiction that $\sqrt{2} + \sqrt{6} < \sqrt{15}$
117999
Prove by contradiction (not using a calculator) that $\sqrt6 + \sqrt2 < \sqrt{15}$?
62485
How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
88188
Explain proof by contradiction.
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
67605
Different proof that $\sqrt{2}$ is irrational
147666
How to prove that either $2^{500} + 15$ or $2^{500} + 16$ isn't a perfect square?
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
133382
Proof that $a+b+\frac{1}{1+\sqrt{ab}}\geq\frac{5}{2}$
114506
Expansion of $(1+\sqrt{2})^n$
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
90276
Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
92226
Prove $\sqrt6$ is irrational
130027
Give a direct proof of the fact that $a^2-5a+6$ is even for any $a \in \mathbb Z$
68838
Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
14386
Proof of an equality involving cosine $\sqrt{2 + \sqrt{2 + \cdots + \sqrt{2 + \sqrt{2}}}}\ =\ 2\cos (\pi/2^{n+1})$
120093
Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction