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Rationalize the Denominator. "Rationalizing the denominator" is when we move a root (like a square root or cube root) from the bottom of a fraction to the top.Why do we rationalize the denominator?
The main reason for "rationalizing" denominators is that when we add fractions we have to get common denominators. And that is typically easier if there are no square roots in the denominators. However, there are times when we want to rationalize the numerator.Do you always have to rationalize the denominator?
Technically no. The general reason why it is desirable, is to have a standard form. If for example you look a trig ratios that have radicals, these are given with rationalized denominators, so it makes it easier to recognize these ratios when you rationalize the denominator in your calculations.