Squares and Square Roots
Simplification of Radical Terms
A radical term is any term that has at least one radical in it. Radical terms can be messy, so we want to write them in the simplest way possible. It's probably also a good idea to fit them with a bib to catch any wayward mashed banana.
Like karate, we only use radicals when we need to. If a radicand is a perfect square, we scrap both the radicand and its radical and write the square root in their place. This is the same thing we did in the previous section when we found square roots, but now we're calling it "simplifying." We've got like a million more names for it, so hit us up any time. We're a river to our people.
To simplify the radical term if a radicand is not a perfect square, we write an equivalent expression in which
- there is only one radical, and
- the radicand has no factors that are perfect squares.
We use multiplication and division to perform this simplification. That's the end of this section. We'll celebrate by starting a new one.