- #1

mathdad

- 1,283

- 1

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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- MHB
- Thread starter mathdad
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In summary, rationalizing the denominator is unnecessary for most calculations, but it may be required by teachers or electronic grading systems. It can also help with significant digit issues and computation efficiency. Some people enjoy the tedious practice and it may be emphasized in certain math courses.

- #1

mathdad

- 1,283

- 1

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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- #2

tkhunny

- 256

- 0

RTCNTC said:

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?

- #3

mathdad

- 1,283

- 1

Rationalizing a numerator or denominator means to rewrite it in a form that does not contain any square roots or other radical expressions.

Rationalizing the numerator or denominator allows us to simplify or evaluate expressions involving square roots or other radical expressions more easily.

To rationalize a numerator or denominator, we multiply it by a cleverly chosen form of 1 that eliminates any radical symbols. For example, to rationalize the denominator of 1/√2, we would multiply by √2/√2, which gives us √2/2 as the new denominator.

There are several methods for rationalizing a numerator or denominator, including multiplying by a conjugate, using the difference of squares formula, or using the rationalizing factor for higher roots.

We typically need to rationalize a numerator or denominator when simplifying or evaluating expressions involving square roots or other radical expressions. It may also be necessary when solving equations or graphing functions involving square roots.

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