When subtracting radicals the steps involved are essentially the same as those involved in adding radicals, and should only be attempted once simplifying radicals is fully understood.
Your child 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.
Remember this rule when adding and/or subtracting, and you can't go wrong!
Only 'Like' radicals can be added or subtracted! When you are presented with a problem, simply reduce each radical to its lowest form
and then operate (ie. add or subtract) as indicated. Just like you did when you learned how to add and subtract fractions! Only like with like!
Follow along with this worked example to see how we add these two radical numbers.
Example 
Steps to Subtract 
Confirm you are subtracting like terms (identical radicals). We DO NOT have Identical radicals, so we must simplify them so we can move forward. 

We can see that 18 = 9 x 2 (where 9 is equal to the perfect square of 3)  we apply rule 1 of radicals. We can see that 32 = 16 x 2 (where 16 is equal to the perfect square of 4)  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 . Root(ab) = root a x root b Now we simply 'tidy things up'. 

We have now simplified the radicals so they are all "alike" Now we operate as indicated. 3 + 8  1 = 10 We have now completed the problem 

SOLUTION 
As you can see from this worked example  the skill to subtracting radicals, is not the subtraction process, but the process of identifying perfect squares or perfect cubes and being able to simplify the radical to its lowest terms. Once your child has successfully completed a number of these adding and subtracting radical numbers they will never make them anxious again.
Radicals 
Exponents

Monomials 
Properties of Arithmatic 
Polynomials

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