Radicals With Like Terms
• Recall that you can add two expressions if they are like terms.
5 7x x
This process is based on the distributive property, which was shown in the second step.
• Example 1
5 7 x 12x
• In the same way we add two radical expressions if they are like terms.
5 7x x
These terms were like since both radicals had the same index (2 in this case), and the same radicand.
• Example 2
5 7 x 12 x
You are encouraged to leave out the middle step.
• Example 3
Simplify: 2 2 24 4 45 3 12 3 3x x x
Note that all three radicals have the same index …
… and the same radicand.
Add and subtract the coefficients to get …
245 12 1 3x 246 3x
• Sometimes it is necessary to simplify the radicals first in order to create like terms.
4 2 2 23 32 24 9 3x x y x xy
• Example 4
Simplify:
3 2 2 23 32 8 3 9 3x x x y x xy
3 2 2 23 32 8 3 9 3x x x y x xy
3 3 2 2 23 32 8 3 9 3x x x y x xy
2 2 23 32 2 3 9 3x x x y x xy
2 2 2 23 34 3 9 3x xy x xy
2 235 3x xy
Like Terms
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