You may want to review simplifying roots first.
When simplifying an expressions with roots in it, there are two rules to keep in mind. One is the one you've already seen, which tells us (say) that √12 = 2√3. The other is that you can combine two terms which have like radicals, which just means that they're the same except for the number in front. For example, 2√3 + 5√3 = 7√3. This also works for subtraction, so 2√3 − 5√3 = −3√3. Remember, this only works because the ‘√3’ bits are the same. Thus, 2√2 + 5√3 doesn't simplify.
These rules work the same way for higher roots. However, they don't combine; 2√2 + 5 3√2 doesn't simplify.