The process is the same for addition and subtraction.
The process is totally different for like and unlike terms.
to simplify the radicand
A radical integer is a number obtained by closing the integers under addition, multiplication, subtraction, and root extraction.
Radical (3x) = radical(x) * radical(3).
The answer depends on the form of the radical expression.
"rationalizing" the denominator
radical expressiona radical expression
Radical like terms are expressions that contain the same type of radical, meaning they have the same index and the same radicand (the number or expression inside the radical). For example, ( \sqrt{2} ) and ( 3\sqrt{2} ) are like terms because they both involve the square root of 2. However, ( \sqrt{2} ) and ( \sqrt{3} ) are not like terms since their radicands differ. Like terms can be combined through addition or subtraction.
A rational expression is an expression that contains a radical, i.e., a root.
10*radical(2).
They can always be combined for multiplication. For division, the only requirement is that the denominator is not 0. For addition and subtraction the terms, after simplification, must have identical radicals.So, for example, sqrt(18) + sqrt(50) can be simplified to 3*sqrt(2) + 5*sqrt(2) and that simplifies to 8*sqrt(2).
A radical expression is an expression that involves a square root, cubic root, etc.
To eliminate the radical in the denominator.