Step 2: Multiply both the numerator and the denominator. Remember that you can multiply numbers

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1 Rationalizing Denominators Here are the steps required to rationalize the denominator containing one terms: Step 1: To rationalize the denominator, you need to multiply both the numerator and denominator by the radical found in the denominator. The reason for this is because when you multiply a square root by itself the radical will disappear. Step 2: Multiply both the numerator and the denominator. Remember that you can multiply numbers outside the radical with numbers outside the radical and numbers inside the radical with numbers inside the Step 3: Simplify the radicals. Step 4: Reduce the fraction, if you can. You can only reduce numbers that are outside the radical with other numbers that are outside the Example 1 Rationalize the Denominator:! " radical found in the denominator. Step 4: Reduce the fraction, if you can. In this case, the we cannot reduce, so the answer is:

2 Example 2 Rationalize the Denominator: #$ %& radical found in the denominator. Example 3 - Rationalize the Denominator: $& ## ' #(& Step 1: To rationalize the denominator, you need to multiply both the numerator and denominator by the radical found in the denominator. Step 2: Multiply both the numerator and the denominator. Remember that you can multiply numbers outside the radical with numbers outside the radical and numbers inside the radical with numbers inside the

3 Example 4 - Rationalize the Denominator: )&* + '& '' Step 1: To rationalize the denominator, you need to multiply both the numerator and denominator by the radical found in the denominator. Step 2: Multiply both the numerator and the denominator. Remember that you can multiply numbers outside the radical with numbers outside the radical and numbers inside the radical with numbers inside the The previous 4 examples showed how to rationalize the denominator if the denominator was a square root. What do you do if the denominator contains a cube root, a fourth root, or any other index? Rather than try and figure out what terms will create a perfect cube or higher, I will do the problems similar to how I did the first four examples. We still need to multiply both the numerator and denominator by the radical found in the denominator, but we will need to multiply more than once. To make a cube root disappear, we will need to multiply by the radical found in the denominator twice. This will give us a total of three radicals that are the same and if you take a cube root and multiply it by itself three times (or cube it) the radical will disappear. To make a fourth root disappear, we will need to multiply by the radical found in the denominator three times. This will give us a total of four radicals that are the same and if you take a fourth root and multiply it by itself four times (or raise it to the fourth power) the radical will disappear. You would do the same sort of thing for fifth roots, sixth roots, etc.

4 Example 5 - Rationalize the Denominator: %,!, "& radical found in the denominator. In this case, the radical is a cube root, so I multiplied twice to get three of a kind in the denominator, which will make the radical disappear. Example 6 - Rationalize the Denominator: $&* - "& - +& * Step 1: To rationalize the denominator, you need to multiply both the numerator and denominator by the radical found in the denominator. In this case, the radical is a fourth root, so I multiplied three times to get four of a kind in the denominator, which will make the radical disappear. Step 2: Multiply both the numerator and the denominator. Remember that you can multiply numbers outside the radical with numbers outside the radical and numbers inside the radical with numbers inside the

5 Step 4: Reduce the fraction, if you can. In this case, the we can reduce, so the answer is: Assignment: Label as Rationalizing Denominators 1) '.& " % 2) +&, % %& #$, 3) $ )& $ '#& 4) )&, #'. '(& 5) "& - $ '' #(& - 6) %& * $ ''