Rationalizing
There is an agreement  in mathematics  that we don’t leave a radical   in the denominator  of a fraction.
So how do we change the denominator of a fraction?  (Without changing the value of the fraction, of course.)
The same way we change the denominator of any fraction!  (Without changing the value of the fraction, of course.)
We multiply the denominator by the same number.  and the numerator
By what number to a rational number?  to change it can we multiply
The answer is . . . . . . by itself!
Remember, is the number we square to get  n . we’d better get  n . So when we square it,
In our fraction, to get the radical out of the  denominator,  we can multiply numerator and  denominator by  .
In our fraction, to get the radical out of the  denominator,  we can multiply numerator and  denominator by  .
Because we are changing  the denominator we call this process  rationalizing . to a rational number,
Rationalize the denominator: (Don’t forget to simplify)
Rationalize the denominator: (Don’t forget to simplify) (Don’t forget to simplify)
When there is a binomial with a radical in the denominator of a fraction, you find the conjugate and multiply. This gives ...
Multiply by the conjugate. FOIL numerator and denominator. Next Simplify:
Simplify  ·  =
Combine like terms Try this on your own:
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Rationalizing the denominator

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Rationalizing the denominator

  1. 2. Rationalizing
  2. 3. There is an agreement in mathematics that we don’t leave a radical in the denominator of a fraction.
  3. 4. So how do we change the denominator of a fraction? (Without changing the value of the fraction, of course.)
  4. 5. The same way we change the denominator of any fraction! (Without changing the value of the fraction, of course.)
  5. 6. We multiply the denominator by the same number. and the numerator
  6. 7. By what number to a rational number? to change it can we multiply
  7. 8. The answer is . . . . . . by itself!
  8. 9. Remember, is the number we square to get n . we’d better get n . So when we square it,
  9. 10. In our fraction, to get the radical out of the denominator, we can multiply numerator and denominator by .
  10. 11. In our fraction, to get the radical out of the denominator, we can multiply numerator and denominator by .
  11. 12. Because we are changing the denominator we call this process rationalizing . to a rational number,
  12. 13. Rationalize the denominator: (Don’t forget to simplify)
  13. 14. Rationalize the denominator: (Don’t forget to simplify) (Don’t forget to simplify)
  14. 15. 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.
  15. 16. Multiply by the conjugate. FOIL numerator and denominator. Next Simplify:
  16. 17. Simplify · =
  17. 18. Combine like terms Try this on your own:

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