Study Guide

Squares and Square Roots Introduction

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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.

Squares and Square Roots Resources


Math is Fun: Squares and Square Roots
Here is a fun, colorful, and highly visual way to understand and practice working with squares and square roots. And it doesn’t cost you a penny! You know, because money is the square root of all evil.

The Math Page: Simplifying Radicals
As we all know, terms with square root symbols in them are ugly. It’s nice to have a way to simplify those suckers, and maybe even eliminate those symbols altogether if we get lucky. Fingers crossed…

PurpleMath: Solving with the Quadratic Formula
Let this site help you understand one of the most important formulas ever devised. That "E = mc2" was a pretty good one, too, but the guy who came up with that was a little crazy-looking. Are we really sure he knew what he was talking about?


Mathgirl: Multiplying and Dividing Radicals
Tired of all those male voices narrating the algebra videos? Allow us to introduce you to Mathgirl, who will walk you through the process of multiplying and dividing radicals. And without all that nauseating testosterone.

MathMeeting: Solve Quadratic Equations Using Quadratic Formula
The comments on this video say it all. If you’re getting stuck on the quadratic formula and need a little extra help to wrap your brain around it, this is where you’ll find it. Still, you should probably do a few light brain exercises first so you don’t pull anything.

Math with Mister A: Multiplying Radicals
This is part one of a two-part video on multiplying radicals. If you like this one, make sure to see the sequel. It isn’t as good as the original, but sequels rarely are. Yes, The Matrix, we're looking at you.

Games and Tools

Fact Monster: Table of Squares and Square Roots
This helpful table shows you the square and square root of every single number between 1 and 100 for your quick and easy reference. They wanted to include an even bigger table, but it never would've fit through the kitchen doorway.

Math-Play: Square Roots Game
Solve square root problems to work your way up the ladder—from $100 to $1,000,000! Don’t bother holding your hands by the USB port waiting for the money to be dispensed, though. This is only for pretend.

Math-Play: Pythagorean Theorem Game
The wizard in this game really, really wants you to solve all of these Pythagorean Theorem problems. Please make him proud. He has little else to live for.

Basic-Mathematics: Pythagorean Theorem Word Problems
The Pythagorean Theorem shows up in word problems all the time because of how applicable it is to real-life situations. See all those triangles floating past your window right now? That's what we're talking about.

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