MHB Rationalize Numerator & Denominator

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Rationalizing the denominator is often considered a convention in mathematics, though it may not be strictly necessary. Fractions can technically have square roots in the denominator, but doing so can complicate calculations. Rationalizing the numerator is less common but may be required in specific contexts. Compliance with these practices is important, as teachers and electronic grading systems may not accept non-rationalized forms. Ultimately, rationalization aids in precision and clarity in mathematical expressions.
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1. Why must we rationalize the denominator?

2. Are fractions not allowed to have square roots in the denominator?

3. When is it necessary to rationalize the numerator?
 
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RTCNTC said:
1. Why must we rationalize the denominator?

2. Are fractions not allowed to have square roots in the denominator?

3. When is it necessary to rationalize the numerator?

Substantially, it is unnecessary. It may sometimes be called "convention".

Secondarily, never pass up an opportunity to get better at something useful through practice - even tedious practice.

Thirdly, Teachers and graders may require it. Comply, or get it wrong.

Fourthly, electronic grading systems may not recognize the answer, otherwise.

Fifthly, there are some significant digit issues and machine considerations. Division by an irrational number can be far more costly than division by an integer.

Convinced?
 
Thank you. When I took precalculus in 1993, the professor made a BIG DEAL about rationalizing the denominator, and the numerator of certain functions. Rationalizing can be tedious but I really enjoy the work. I was just curious as to why it is a big concern in math courses.
 

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