4.6 SAT Math - Rationalizing Denominators

It's considered bad form to leave a square root in the denominator, so answer choices with square roots will usually be rationalized, which means have a whole number in the denominator.

To get rid of a square root in the denominator, you have to remember that a square root times itself equals whatever number is under the square root symbol: so

and also how to create equivalent fractions, which is by multiplying the numerator and denominator by the same number. (That is, by the way, the nice thing about math: the numbers will get uglier the more you know, but the rules never change.) We'll use that information to clean up the square root fraction from the last example above:

Multiply the fraction both top and bottom by whatever square root is on the bottom:

And then simplify the resulting fraction if necessary:

-SAT Math Hint: Don't rationalize denominators until you get to the answer choices to look for your answer!  The answers on this test will sometimes be given in square root form, and sometimes in their approximate decimal equivalent.  Save any extra work until you're sure you need to do it.  If the answers are in decimal form, simply type the square root answer you found into your calculator and see what comes up.

-SAT Math Tip: Keep in mind that square roots of numbers greater than 1 represent a number greater than 1!  Many, many people think of square roots as if they were decimals less than 1, forgetting that square roots do contain a significant value.  If you keep this in mind, you should be able to eliminate at least one or two answer choices on this fact alone, answer choices that are designed to trick those students that forget.  This is most helpful on geometry questions.