Читать книгу SAT Math For Dummies with Online Practice - Mark Zegarelli - Страница 56

In some cases, you can simplify a radical by factoring it and then evaluating one of the factors as a whole number. This is always the case when the value inside the radical is divisible by a square number, such as 4, 9, 16, 25, and so forth.

For example, here are three radicals that can be simplified by factoring out and then simplifying this value to 2:

Similarly, you can simplify the following three radicals by factoring out and then simplifying this value to 3:

These three radicals can be simplified by factoring out :

And these three can be simplified by factoring out :

An SAT question may ask you to simplify a radical. For example:

Which of the following is the most simplified form of ?

(A)

(B)

(C)

(D)

The number 72 is divisible by 9, so you can factor and simplify as follows:

Although is equivalent to , the question asks you to find the most simplified form of the radical. To do this, notice that 8 is divisible by 4, so you can further factor and simplify as follows:

This result is the most simplified form of , so Answer C is correct. (You can also find this answer directly as .)

Other opportunities for simplifying radicals may arise when working with the quadratic formula, which includes a radical. In 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.