Operations with Radicals |
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Simplification Addition and Subtraction Multiplication Division
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Simplification of Radicals | Rule | Example | |
Use the two laws of radicals to
SHORTCUT:
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Simplification Addition and Subtraction Multiplication Division |
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Addition and Subtraction of radicals | Rule | Example | |
Simplify all radicals. Combine only
like radical terms: Combine like radicals by combining the coefficients of the radical terms. The coefficient is the factor that sits outside the radical to the left. |
Note:
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Example 1:
Example 2:
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Simplification Addition and Subtraction Multiplication Division |
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Multiplication of radicals | Rule | Example | |
If the indices are the same
NOTE: You may simplify the radicals before multiplying. However, you may need to simplify the radical again once you have found the product.
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Example 1:
Example 2:
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Simplification Addition and Subtraction Multiplication Division |
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Division | Rule | Example | |
NOTE: A simplified radical contains no fractions and no radicals in the denominator. | |||
Division
Type I:
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Division
Type II: |
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(a + b) and (a - b) are conjugates: middle signs are opposite. Multiplying
by conjugates gives the difference of squares:
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Simplification Addition and Subtraction Multiplication Division |
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