Arithmetic Course/Number Operation/Root

      Root

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

      Rules

      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

      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)
      Last modified on 1 May 2011, at 16:32