rel="nofollow" href="#ucf64812e-0880-54db-87fd-4744bbaa46f4">Chapter 3, I show you how to use this formula to solve quadratic equations. And then in Chapter 12, you use it again to find the roots of quadratic functions.
Adding and subtracting radicals
You can only add equivalent radicals. For example:
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You can add radical expressions that have the same radical parts by adding coefficients. For example:
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You can also subtract radicals in the same way:
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In some cases, you can add or subtract radical expressions with non-equivalent radical parts by simplifying them using the factoring method I describe in the previous section. For example, here’s an SAT question that depends upon your understanding this idea:
(A)
(B)
(C)
(D)
Begin by factoring
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Now, rewrite
So Answer C is correct.
Rationalizing radicals in the denominator
In some cases, when a radical appears in the denominator of a fraction, an SAT question will require you to rationalize the denominator — that is, find an equivalent form of that fraction with an integer in the denominator.
To rationalize the denominator of a fraction, multiply both the numerator and denominator by the radical that’s in the denominator. For example, here’s how you rationalize
In some cases when rationalizing, you may need to simplify the result. For example, here’s how you rationalize
This result can be simplified by dividing both the numerator and the denominator by 2:
Understanding Algebra Terminology
Look over the following list of 12 words:
| Algebra | Arithmetic | Coefficient | Constant |
| Equation | Expression | Identity | Inequality |
| Polynomial | Term | Variable | Zebra |
First of all, ignore the word zebra. I just put that one in to fill out the last row. Zebras have nothing at all to do with math. They can’t even do math.
As for the other 11 words, even though they may get thrown around a lot in whatever math class you’re currently taking, you may not be really sure about some (or all!) of them.
You could ask your teacher to explain them. In fact, I encourage you to do that. Even so, you probably won’t. After years of teaching, I get that most of my students just don’t feel comfortable asking questions about stuff that they think they “should already know.”
That’s why I’m here: for starters, to help you succeed on the SAT. But beyond this, so that the next time your teacher asks for a volunteer to identify the coefficient of the third term in the right-hand expression of the equation they just wrote on the board, you’ll be able to raise your hand with pride and confidence.
Algebra and arithmetic
Arithmetic is the mathematics of numbers and operations upon them — essentially, number crunching. I cover a lot of this material in Basic Math & Pre-Algebra For Dummies (Wiley). When you know how to perform the operations in a given problem in the correct
