How to check if $n^2$ will square root evenly without square rooting $n^2$
107781
Detecting perfect squares faster than by extracting square root
36664
How is the square root function implemented?
107142
If $(x_n) \to x$ then $(\sqrt[n]{x_1x_2\cdots x_n}) \to x$
110226
How can I find the square root using pen and paper?
134927
How can a square root be defined since it has two answers?
79103
Check if a number is a perfect square
97952
Square root of 1 is (not) -1
6582
Prove the existence of the square root of $2$.
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
82462
Square Root Algorithm
44391
How can I prove $n - 2\sqrt{n} = \Theta(n)$
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
136366
Show that if $2+2\sqrt{28n^2+1}$ is an integer then it must be perfect square.
148163
Show that if m/n is a good approximation of $\sqrt{2}$ then $(m+2n)/(m+n)$ is better
145558
Prove that $2^n+3^n $ is never a perfect square
47060
Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$
142768
Approximation of $\sqrt{2}$