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• Quadratic formula
  <cmath>x+\frac{b}{2a}=\pm\sqrt{\frac{b^{2}-4ac}{4a^{2}}}=\frac{\pm\sqrt{b^{2}-4ac}}{2a}</cmath> <cmath>x=-\frac{b}{2a}+\frac{\pm\sqrt{b^{2}-4ac}}{2a}=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}</cmath>
  2 KB (290 words) - 16:55, 19 February 2024
• Sieve of Eratosthenes
  ...umber | composite]], then it has a prime [[divisor]] not exceeding <math>\sqrt n</math>.
  1 KB (212 words) - 21:16, 7 December 2007
• Imaginary unit
  ...ex number itself. It has a [[magnitude]] of 1, and can be written as <math>1 \text{cis } \left(\frac{\pi}{2}\right)</math>. Any [[complex number]] can b #<math>i^1=\sqrt{-1}</math>
  2 KB (321 words) - 15:57, 5 September 2008
• Absolute value
  * (Alternative definition) <math>|x| = \sqrt{x^2}</math> ...ex number]]s <math>z</math>, the absolute value is defined as <math>|z| = \sqrt{x^2+y^2}</math>, where <math>x</math> and <math>y</math> are the real and i
  2 KB (368 words) - 10:37, 5 January 2009
• Rational approximation of famous numbers
  ...<+\infty</math>, the [[inequality]] <math>\left|x-\frac pq\right|\ge \frac 1{q^M}</math> holds for all sufficiently large denominators <math>q</math>. Suppose that there exist <math>0<\beta<\gamma<1</math>, <math>1<Q<+\infty</math>
  8 KB (1,431 words) - 13:48, 26 January 2008
• LaTeX:Symbols
  ...setminus</math>||\setminus||<math>\wr</math>||\wr||<math>\sqrt{x}</math>||\sqrt{x} ...rc}||<math>\triangledown</math>||\triangledown||<math>\sqrt[n]{x}</math>||\sqrt[n]{x}
  16 KB (2,324 words) - 16:50, 19 February 2024
• 2006 AMC 12B Problems/Problem 21
  \mathrm{(A)}\ \frac {16\sqrt {2006}}{\pi} \mathrm{(C)}\ 8\sqrt {1003}
  2 KB (339 words) - 13:15, 12 July 2015
• 3D Geometry
  ...he 30-60-90 triangle, or the Pythagorean Theorem, to find that <math> x = \sqrt{3} </math> units.
  2 KB (263 words) - 12:29, 30 December 2023
• Srinivasa Ramanujan
  <math>\frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum^\infty_{k=0} \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}</mat
  496 bytes (62 words) - 23:16, 24 February 2007
• 2004 AIME II Problems/Problem 11
  ...xact opposite side of the cone whose distance from the vertex is <math>375\sqrt{2}.</math> Find the least distance that the fly could have crawled. ...<math>R=\sqrt{r^2+h^2}=\sqrt{600^2+(200\sqrt{7})^2}=\sqrt{360000+280000}=\sqrt{640000}=800</math>. Setting <math>\theta R=C\implies 800\theta=1200\pi\impl
  2 KB (268 words) - 22:20, 23 March 2023
• 1986 AIME Problems/Problem 1
  ...he sum of the solutions to the equation <math>\sqrt[4]{x} = \frac{12}{7 - \sqrt[4]{x}}</math>? Let <math>y = \sqrt[4]{x}</math>. Then we have
  688 bytes (104 words) - 13:34, 22 July 2020
• 1987 AIME Problems/Problem 9
  C = (21*sqrt(3),0);
  1 KB (200 words) - 18:44, 5 February 2024
• 1989 AIME Problems/Problem 12
  ...ontsize(10)); label("$7$",A--C,2*dir(210),fontsize(10)); label("$18$",A--D,1.5*dir(30),fontsize(10)); label("$36$",(3,0),up,fontsize(10)); ...h>\triangle CDM</math>. The formula for the length of a median is <math>m=\sqrt{\frac{2a^2+2b^2-c^2}{4}}</math>, where <math>a</math>, <math>b</math>, and
  2 KB (376 words) - 13:49, 1 August 2022
• 2003 AIME I Problems/Problem 8
  <cmath>d=\frac{-3a + \sqrt{9a^2+120a}}{2}.</cmath> <cmath>a=\frac{-120 + \sqrt{14400+36x^2}}{18}</cmath>
  5 KB (921 words) - 23:21, 22 January 2023
• 2003 AIME II Problems/Problem 10
  ...qrt{b}+\sqrt{b+60}=\sqrt{c}</math>. Square both sides to get <math>2b+60+2\sqrt{b^2+60b}=c</math>. Thus, <math>b^2+60b</math> must be a square, so we have
  1 KB (218 words) - 14:14, 25 June 2021
• 2005 AMC 10B Problems/Problem 4
  ...al numbers <math>a</math> and <math>b</math>, define <math>a \diamond b = \sqrt{a^2 + b^2}</math>. What is the value of ...\textbf{(B) } \frac{17}{2} \qquad \textbf{(C) } 13 \qquad \textbf{(D) } 13\sqrt{2} \qquad \textbf{(E) } 26</math>
  833 bytes (110 words) - 13:58, 24 July 2022
• Incircle
  ...formula above can be simplified with Heron's Formula, yielding <math>r = \sqrt{\frac{(s-a)(s-b)(s-c)}{s}}.</math> *The [[area]] of the [[triangle]] by [[Heron's Formula]] is <math>A=\sqrt{s(s-a)(s-b)(s-c)}</math>.
  2 KB (384 words) - 18:38, 9 March 2023
• Hypotenuse
  ...a triangle with legs of length <math>a</math> and <math>b</math> is <math>\sqrt{a^2 + b^2}</math>.
  810 bytes (133 words) - 19:02, 15 October 2018
• 1969 Canadian MO Problems/Problem 9
  ...>1,</math> the length of the shortest side is less than or equal to <math>\sqrt{2}</math>. ...ossible. Thus, at least one of the sides must have length less than <math>\sqrt 2</math>, so certainly the shortest side must.
  795 bytes (138 words) - 22:42, 17 November 2007
• Parallel
  <math>\sqrt{\frac{(y_2-y_1)^2}{m^2+1}}</math>
  2 KB (326 words) - 12:11, 21 May 2009

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