Radicals separate themselves from rational numbers because of the root sign (√, ∛, etc.) or fractional exponents (½, ⅓, etc.). In an expression they stand out like different powers of a variable in a polynomial.
For example, 2x3+5x2+x-1 has separate terms because the different powers of x can't be combined into fewer terms. Similarly, in 3√2+7∛6+2√3+6√7-10 the terms can't be combined into fewer terms because the radicals are all different. There is no other way to represent this expression without evaluating the radicals to some approximation (they can never be exactly evaluated because by definition they never resolve into a rational fraction or mixed number).
Two radicals are alike, or are like radicals, only when, after reduction to the simplest form, they each involve the same root radical. For example, the first two radicals in √8, √12, √3, √2 can be respectively reduced to 2√2 and 2√3. Therefore √8+√2=2√2+√2=3√2; √12+5√3=2√3+5√3=7√3. This is similar to adding to identical powers of a variable: 3y3+7y3=10y3.
Another form of radicals is, for example, 4⅓, 5½, 60.75, or 2⅗. Take 4⅓+2⅗, which can be written:
2⅔+2⅗. Although the base is 2 in each case, they cannot be combined into a single term because the powers are different, just like adding x3 to x4, which cannot be reduced to a single term, because x is the common base but the exponents differ.
x2√2+x2√3 can't be reduced to a single term (although the expression can be factorised) without evaluating the radicals by approximation. So variables and radicals can be mixed. On the other hand, 2x2+3x2 does reduce to the single term 5x2, because no radicals are involved.
When you see a radical, make sure it really is a radical. For example, √(25x2y) reduces to 5x√y, so only √y is a radical, because the multipliers are perfect squares. Be prepared to factorise what's under the root sign in case there's a hidden perfect square. √(125x5y4)=5x2y2√5x, because 125x5y4=25x4y4 × 5x=(5x2y2)25x.