Combining Like Radical Terms
Adding and subtracting radical expressions is like adding and subtracting
polynomials.
• With polynomials, to add like
terms, we add their coefficients. |
2x + 3x = (2 + 3)x = 5x |
• With radical expressions, to add
like radical terms, we add the
numbers in front of the radicals. |
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Before we can combine radical terms, we sometimes need to simplify the
individual radicals to obtain like terms.
Consider this example: |
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At first glance, we may think we cannot add the radical terms because the
radicands are different. |
However, if we simplify
, we can
combine like radical terms: |
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Example 2
Simplify:
Solution
First simplify
The radicand, 75y, has a perfect
square factor, 25. |
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Replace
with
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Combine the like radical terms,
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Simplify. |
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So, |
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Example 3
Simplify:
Solution
First simplify
The radicand, 54x, has a perfect
cube factor, 27. |
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Replace
|
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Multiply
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Combine the like radical terms
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Simplify. |
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So, |
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