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Simplifying Radical Expressions and Rationalizing

Task 1: Adding and Subtracting Radical Expressions.

a) Simplify the polynomial expressions .

b) Simplify the radical expressions .

c) For the following, rewrite the individual terms if possible in order to get "like terms", and then
simplify the whole expression by adding " like terms ". Example:

Task 2: Multiplying Conjugates .

a) Multiply the polynomial conjugates .

b) Use the same process to multiply the binomials which contain radicals. Remember:

Note that the product of conjugates contains no square roots . This leads to a process of "rationalizing"
( eliminating square roots in ) either the numerator or denominator of an algebraic expression.

Task 3: Rationalizing Denomiators or Numerators

a) Rationalize the denominator by multiplying by one in the form of the appropriate conjugate divided by
itself.

b) Rationalize the numerator by multiplying by one in the form of the appropriate conjugate divided by
itself

 

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