Sohcahtoa Prime is the first of a vast giant robot army that Mr. Ward has built. He is named after the great trigonometry mnemonic, SOHCAHTOA (Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse and Tangent is Opposite over Adjacent). He takes great pride in his name as it helps him remember his calculations of distance when using his disintegration beam upon those who annoy him.
SOCkET is a different model, but very efficient and helps Sohcahtoa Prime derive his answers. SOCkET takes his name from another great trigonometry mnemonic, SOCkET (Sine Over Cosine Equals Tangent).
GERMDAS likes to order things around. He begins with Grouping things, Using Exponents and Roots, then he Multiplies and/or Divides, finishing everything off with a round of Addition and/or Subtraction. He prefers to do all of this From Left To Right.
Root hasn't told us his back story, but asks that we not be too negative if we are going to be square. He'll leave the meaning of that up to our imagination.