What is "to extract the root"

Extract \Ex*tract"\, v. t. [imp. & p. p. Extracted; p. pr. & vb. n. Extracting.] [L. extractus, p. p. of extrahere to extract; ex out + trahere to draw. See Trace, and cf. Estreat.]

1. To draw out or forth; to pull out; to remove forcibly from a fixed position, as by traction or suction, etc.; as, to extract a tooth from its socket, a stump from the earth, a splinter from the finger.

   The bee Sits on the bloom extracting liquid sweet.
   --Milton.

2. To withdraw by expression, distillation, or other mechanical or chemical process; as, to extract an essence. Cf. Abstract, v. t., 6.

   Sunbeams may be extracted from cucumbers, but the process is tedious.

3. To take by selection; to choose out; to cite or quote, as a passage from a book.

   I have extracted out of that pamphlet a few notorious falsehoods.
   --Swift.

   To extract the root (Math.), to ascertain the root of a number or quantity.