Simplifying Radicals

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Simplifying Radicals
Binomial Conjugate
Binomial quantity that turns the expression into
a difference of squares.
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Example 1 Binomials Conjugates
A
3
Example 2 Use Binomials Conjugates to
Rationalize
A
B
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SPECIAL FRACTION EXPONENT
The exponent is most often used in the power
of monomials.
Examples Do you notice any other type of
mathematical symbols that these special fraction
exponents represent?
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Special Fraction Exponents, , are more commonly
known as radicals in which the N value represents
the root or index of the radical.
Index
Radical Symbol
Radicals
Radicand
Note The square root or ½ exponent is the most
common radical and does not need to have the
index written.
Steps for Simplifying Square Roots

1. Prime Factorization Factor the Radicand
   Completely
2. Write the base of all perfect squares (PAIRS)
   outside of the radical as product
3. Everything else (SINGLES) stays under the radical
   as a product.

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Operations with Rational (Fraction) Exponents

• The same operations of when to multiply, add,
  subtract exponents apply with rational (fraction)
  exponents as did with integer (whole) exponents
• Hint Remember how to find common denominators
  and reduce.

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2)
3)
4)
5)
6)
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Radicals (Roots) and Rational Exponent Form
Rational Exponents Property
OR
OR
Example 2 Change Radical to Rational Form
A
B
C
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Radicals Classwork
1 4 Write in rational form.
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5 8 Write in radical form.
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8.
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Radicals Classwork 2
Determine if each pair are equivalent statements
or not.
1.
2.
and
and
3.
4.
and
and
6.
5.
and
and
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Simplifying Rational Exponents

• Apply normal operations with exponents.
• Convert to radical form.
• Simplify the radical expression based on the
  index and radicand.

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Radicals Classwork 3
Simplify the following expressions into simplest
radical form
2.
1.
3.
6.
5.
4.
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Change of Base (Index or Root)

• Write the radicand in prime factorization form
• REDUCE the fractions of Rational Exponents to
  rewrite radicals.

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2.
3.
3.
3.
4.
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Change of Base Practice Problems
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