Adding radical expressions

How is adding radical expressions similar to adding polynomial expressions?

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You add the numbers in front of the radical signs, just as you 
add the coefficients in front of the like variables. 

Notice the similarities:

3 cats + 2 cats = 5 cats
3x + 2x = 5x
3√2 + 2√2 = 5√2 

1 dog + 6 dogs - 4 dogs = 3 dogs
x + 6x - 4x = 3x
√5 + 6√5 - 4√5 = 3√5

​See more combining like terms examples here
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