Arithmetic Course/Number Operation/Root

From Wikibooks, open books for an open world
Jump to: navigation, search

Root[edit]

Root is an arithmatic operation opposite to power . If there exists a ^ n = b Then \sqrt{b} = a

Rules[edit]

Square root of zero is

\sqrt{0} =

Square root of one is one

\sqrt{1} = 1

Square root of negative one is an imaginary number j

\sqrt{-1} = j

Identities[edit]

  1. \sqrt{a} \sqrt{-a} = \sqrt{-a^2} = j \sqrt{a^2}
  2. \sqrt{a} \sqrt{a} = a
  3. \sqrt{a} \sqrt{b} = \sqrt{ab}
  4. \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}
  5. \sqrt{a^n} = a \sqrt{a^(n-2)}
  6. (\sqrt{a})^n = a ^(n-2)