Squares and Square Roots Introduction
In this section, we'll cover squares and square roots, also known as radicals. This is not because of their extreme political views, although it might explain why none of them have ever been elected to public office. We've talked a little about squares and square roots here and there; now we'll dive deeper into what they are and how they make geometrical sense. (We'll also talk about what it means to make geometrical sense, in case you were wondering.) Finally, we'll practice manipulating expressions and solving equations that involve radicals. We'll get to the root of these squares if it's the last thing we do.
We'll also introduce a few more ways to solve quadratic equations. We already know how to solve quadratic equations that can be factored, but now we'll turn our attention to solving any quadratic equation with real-number solutions. And they thought they could hide from us because they couldn't be factored. Joke's on them.
Finally, we'll do some word problems and get friendly with the Pythagorean Theorem. Not too friendly, of course; we hear it's seeing Euclid's proof of the infinitude of primes, and it's getting kind of serious. Here's a preview: If you're the kind of person who who hisses and recoils at the sight of word problems (bet that makes math class super fun), we've got the perfect rule to help you beat them. We hope you're ready for this jelly, because here it is:
When in doubt, draw a picture.
In fact, try to channel your inner Bob Ross. We're especially fond of the happy little trees.