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Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. Rationalizing the Denominator
8.4
Rationalizing the Denominator
Rationalize denominators with square roots.
Write radicals in simplified form.
Rationalize denominators with cube roots. 1 2 3
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3. Rationalize denominators with square roots.
Objective 1
Rationalize denominators with
square roots.
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4. Rationalize denominators with square roots.
It is easier to work with a radical expression if the denominators do not contain any radicals.
This process of changing the denominator from a radical, or irrational number, to a rational number is called rationalizing the denominator. The value of the radical expression is not changed; only the form is changed, because the expression has been multiplied by 1 in the form of
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5. EXAMPLE 1 Rationalize each denominator. Solution:
Rationalizing Denominators
EXAMPLE 1
Rationalize each denominator.
Solution:
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6. Write radicals in simplified form.
Objective 2
Write radicals in simplified form.
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7. Write radicals in simplified form.
A radical is considered to be in simplified form if the following three conditions are met.
The radicand contains no factor (except 1) that is a perfect square (in dealing with square roots), a perfect cube (in dealing with cube roots), and so on.
The radicand has no fractions.
No denominator contains a radical.
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8. EXAMPLE 2 Solution: Simplifying a Radical Slide 8.4 - 8
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9. EXAMPLE 3 Simplify Solution: Simplifying a Product of Radicals
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10. EXAMPLE 4 Simplify . Assume that p and q are positive numbers.
Simplifying a Quotient of Radicals
Simplify Assume that p and q are positive numbers.
Solution:
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11. EXAMPLE 5 Simplify . Assume that r and t represent
Simplifying a Radical Quotient
EXAMPLE 5
Simplify Assume that r and t represent
nonnegative real numbers.
Solution:
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12. Rationalize denominators with cube roots.
Objective 3
Rationalize denominators with cube roots.
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13. EXAMPLE 6 Rationalize each denominator. Solution:
Rationalizing Denominators with Cube Roots
Rationalize each denominator.
Solution:
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