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?
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.