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Rationalizing

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**that we don’t leave a radical**

There is an agreement in mathematics that we don’t leave a radical in the denominator of a fraction.

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**So how do we change the denominator of a fraction?**

(Without changing the value of the fraction, of course.)

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**The same way we change the denominator of any fraction!**

(Without changing the value of the fraction, of course.)

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**We multiply the denominator**

and the numerator by the same number.

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By what number can we multiply to change it to a rational number?

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The answer is . . . . . . by itself!

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Remember, is the number we square to get n. So when we square it, we’d better get n.

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In our fraction, to get the radical out of the denominator, we can multiply numerator and denominator by

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In our fraction, to get the radical out of the denominator, we can multiply numerator and denominator by

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**Because we are changing the denominator**

to a rational number, we call this process rationalizing.

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**Rationalize the denominator:**

(Don’t forget to simplify)

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**Rationalize the denominator:**

(Don’t forget to simplify) (Don’t forget to simplify)

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When there is a binomial with a radical in the denominator of a fraction, you find the conjugate and multiply. This gives a rational denominator.

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**Simplify: Multiply by the conjugate. FOIL numerator and denominator.**

Next

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Simplify =

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Combine like terms Try this on your own:

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