Radical Expressions Part 2

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Chapter 8 Continued Radical Expressions and
Equations Multiplication Division of Radical
Expressions When multiplying radical
expressions, you can just put everything thats
under a radical sign together under one big
radical sign. Distributive
Property BE CAREFUL!
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Example 3 Multiply
Example Multiply Notice that when ra
adical expression has two terms, all radicals
disappear when you multiply the expression by its
conjugate. Try this one
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• Radical Expressions in Simplest Form
• A radical expression is in simplest form if
• The radicand contains no factor greater than 1
  that is a perfect square.
• There is no fraction under the radical sign.
• There is no radical in the denominator of a
  fraction.
• is not in simplest form because there is a
  fraction under the radical sign. This can be
  simplified by taking the square root of the
  numerator and the denominator.

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Is not in simplest form because there is a
radical expression in the denominator The way to
simplify is to multiply both numerator and
denominator by
This doesnt always work when there is a two-term
expression with at least one radical term added
to another term.
UGH!
The trick for these types is to multiply the
numerator and denominator by the conjugate.
SIMPLIFIED!
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Solving Equations Containing Radical
Expressions Property of Squaring Both Sides of
an Equation If a and b are real numbers and ab,
then a2b2
Its very important to check your solution
because some solutions actually make the
original equation untrue. Example Notice
that when you get the constants on one side, your
equation says that the radical expression must
equal a negative number. This is impossible!
Therefore there is NO SOLUTION to an equation
like this.
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square both sides This is now a degree 2
equation so put it in standard form, factor it,
then use zero-product rule.
Impossible because the principal square root of a
number can never be negative. Therefore -6 is
not a possible solution.
OK Therefore, only solution is 5
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You try! Solve a
Solve equation and exclude any extraneous
solutions m
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Solve