query: Is there an elementary proof for the monotonicity of $\sqrt x$?
positive_passages.docid: 143122
positive_passages.text: Showing that the square root is monotone
negative_passages.docid: 42976
negative_passages.text: How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
negative_passages.docid: 140841
negative_passages.text: Induction proof of lower bound for $\sum \sqrt n$
negative_passages.docid: 158276
negative_passages.text: Inequality problem involving square roots
negative_passages.docid: 73553
negative_passages.text: How is $a_n=(1+1/n)^n$ monotonically increasing and bounded by $3$?
negative_passages.docid: 84558
negative_passages.text: Prove that the square root of a positive integer is either an integer or irrational
negative_passages.docid: 141895
negative_passages.text: Proving that a sequence is monotone
negative_passages.docid: 152436
negative_passages.text: Are $(x^3)^{1/3} $ and $\sqrt{x^2}$ monomials?
negative_passages.docid: 88425
negative_passages.text: Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
negative_passages.docid: 100947
negative_passages.text: Prove that $\sqrt[n]{n!}$ is increasing and diverges
negative_passages.docid: 86518
negative_passages.text: Does $X$ have a lower bound?
negative_passages.docid: 139674
negative_passages.text: Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
negative_passages.docid: 126074
negative_passages.text: Proof of the irrationality of $\sqrt{3}$ - logic question
negative_passages.docid: 140409
negative_passages.text: Prove that $\sqrt{n} > \ln n$
negative_passages.docid: 67605
negative_passages.text: Different proof that $\sqrt{2}$ is irrational
negative_passages.docid: 14448
negative_passages.text: Elementary proof that $|x|^p$ is convex.
negative_passages.docid: 156766
negative_passages.text: Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$