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No, you can also use conjugates with more than one radical term. For example, if the denominator is root(2) + root(3), you can use the conjugate root(2) - root(3) to rationalize the denominator.
Sodium is not a radical, it is an element. Chemists use the term radical to refer to small groups of atoms, such as the nitrate or phosphate or ammonium radicals, which tend to remain together as a group even when undergoing chemical reactions. A single atom, such as a sodium atom, is not a radical, it is just an element.
A "radical" equation is an equation in which at least one variable expression is stuck inside a radical, usually a square root. The "radical" in "radical equations" can be any root, whether a square root, a cube root, or some other root. Most of the examples in what follows use square roots as the radical, but (warning!) you should not be surprised to see an occasional cube root or fourth root in your homework or on a test.
The role that radical numbers play in your profession depend on what profession you are in. Careers in science and engineering use radical numbers in various ways including to prove concepts and to calculate limits and dimensions.
In the simplest case, it is use to find the diagonal length of a unit square.