a b n a n b n a m a m n Remarks A radical is in simplest form if all the

A b n a n b n a m a m n remarks a radical is in

This preview shows page 1 out of 1 page.

ab=nanbnam=amnRemarks.A radical is insimplest formif all the following condi-tions are satisfied:The radicand is positive.The radicand of a radical of indexnhas no factor which is aperfectnth power.There are no fractions under the radical sign.There is no radical in the denominator of a rational expression.The index of the radical is the smallest possible.Operations Involving Radical ExpressionsAddition and Subtraction of Radical ExpressionsRadicals with the same index and radicand can be added or sub-tracted.Multiplication and Division of Radical ExpressionsIf radicals have the same index, we usena·nb=nabandnanb=nrabIf radicals have different indices, we first make their indices the sameby finding the LCM of all the indices.Rationalization of Radical ExpressionsTo rationalize the denominator,If the denominator is a single radical expression, multiply boththe numerator and denominator by an expression that willmake the radicand of the denominator a perfect power of theindex.If the denominator consists of two or more radical expres-sions, use the special products:(x-y)(x+y) =x2-y2,(x+y)(x2-xy+y2) =x3+y3, and (x-y)(x2+xy+y2) =x3-y3.
Background image

You've reached the end of your free preview.

Want to read the whole page?

  • Fall '16
  • Algebra, Exponents, Nth root, Subtraction of Radical Expressions, Division of Radical Expressions

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture