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Lesson 158: Rationalizing the Denominator
In this quick and easy lesson we'll learn what to do when we have a fraction with a radical in the denominator
For a fraction to be considered simplified, it must not have a radical in the denominator. If you have such a fraction, there is a very simple procedure to be followed. It is known as rationalizing the denominator.
Before
we begin, it is important to review some properties of radicals
which we have already learned. Remember that a product under a
radical sign can be split up into a product of radicals, or
vise-versa, as shown at left. We also know that a·a can be
represented as a2. We also know that if we square a
number, and then take the square root of that result, we're back to
the original number. Be sure that you fully understand all of
those properties of radicals.
Let's say we simplify an expression, and end up with 2/(√3). We cannot leave a radical in the denominator. In this case, all we need to do is multiply the fraction by (√3)/(√3). We're allowed to do that, since we're really only multiplying by 1. Doing so, we get 2(√3) in the numerator, and the denominator becomes 3, following the rules above. The simplified fraction is then 2(√3) / 3. Follow this procedure whenever you have a radical in the denominator.
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