query: Are all the square roots of non-square numbers surds?
positive_passages.docid: 1383
positive_passages.text: How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
negative_passages.docid: 37189
negative_passages.text: Exponent of a number is a square root?
negative_passages.docid: 134927
negative_passages.text: How can a square root be defined since it has two answers?
negative_passages.docid: 109305
negative_passages.text: Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
negative_passages.docid: 150576
negative_passages.text: When is an Integer a Rational Number, and are All Ratios Rational, Even $\frac{\sqrt{7}}{2}$?
negative_passages.docid: 34227
negative_passages.text: Continued fraction of a square root
negative_passages.docid: 39170
negative_passages.text: Existence of square root
negative_passages.docid: 17886
negative_passages.text: Values of square roots
negative_passages.docid: 28228
negative_passages.text: Is a prime factor of a number always less than its square root?
negative_passages.docid: 2705
negative_passages.text: How many roots have modulus less than $1$?
negative_passages.docid: 3955
negative_passages.text: Square roots -- positive and negative
negative_passages.docid: 73612
negative_passages.text: Is there a Non-prime Number that is Divisible only by Numbers Greater than its Square Root?
negative_passages.docid: 7898
negative_passages.text: Finding square root without using sqrt function?
negative_passages.docid: 34491
negative_passages.text: Is there a way to show that $\sqrt{p_{n}} < n$?
negative_passages.docid: 60261
negative_passages.text: Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$
negative_passages.docid: 66127
negative_passages.text: Square roots not on same height
negative_passages.docid: 49750
negative_passages.text: Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$