• Graham's law states that the rate of effusion of a gas is inversely proportional to the square root of its molecular mass, so in a box containing a semi-permeable membrane and a mixture of two gases, the lighter molecules will pass out of the container more rapidly than the heavier molecules.
  • Wikipedia: Manhattan Project
  • More recently, a four-bit circuit was demonstrated that can compute the square root of the integers 0–15, using a system of gates containing 130 DNA strands.
  • Wikipedia: DNA nanotechnology
  • The character Sky Silvestry when taken over mimics the speech patterns of The Doctor by repeating, in synchronism, the square root of pi to 30 decimal places.
  • Wikipedia: Pi
  • The game of checkers was solved in 2007, but it has roughly the square root of the number of positions in chess.
  • Wikipedia: First-move advantage in chess