Adding Radicals should only be attempted once simplifying radicals is fully understood. Your kid should also know the rules for radicals and have had a chance to practice applying these rules.
Your student also has to be comfortable identifying perfect squares and perfect cubes,the skill required when simplifying radicals.
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Remember this rule when adding, and you can't go wrong!
Only 'Like' radicals can be added!

It can't be done! Right? .... Wrong! It can be done  and what they were thinking was  "let the games begin!"
And this is something your student must now get used to! Algebra is a game. It is simply about manipulating numbers (while ALWAYS obeying the rules) to make them do what YOU want them to do!
Follow along with this worked example to to watch the mathematical magic unfold and see how we add these two radical numbers.
We DO NOT have Identical radicals, so we must simplify them so we can move forward.  
We can see that 48 = 12 x 4 (where 4 is equal to the perfect square of 2)  we apply Rule 1 of radicals.  
We apply Rule 1 of radicals again, to find the root of the perfect square and bring it outside the radical.  
We could now add these two radical numbers to get an answer of 13Root12. But we see that 12 is also composed of the products of 4 and 3; 4 again being the result of the perfect square 2, so we are not finished yet!  
We apply Rule 1 of radicals again this time to BOTH numbers.  
We now tidy up everything, before we add to ensure no errors.
 
We are NOW adding 'Like' radicals 6 + 20 = 26 6root3 + 20root3 = 26root3 
No  it is all about familiarity and confidence with regards to 'seeing' the factors of the root and knowing perfect squares and cubes.
Had we taken a little more time looking at these root, we could have noticed that:
 
Had we been more aware of our Perfect Squares and Factors, we could have gotten to this stage in one move! 
As you can see from this worked example  the skill to adding radicals, is not the addition process, but the process of identifying perfect squares or perfect cubes, knowing how to factorize numbers and knowing the Rules of Radicals to simplify the radical to its lowest terms.
Once your child has successfully completed a number of these problems, adding and subtracting radical numbers will never again make them anxious.
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