Sir when we rationalize the equation nemonitor should division both nemonitor and denominator but there denominator should division both why
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Answer:
You’ve heard it time and time again, “Rationalize the denominator. Make sure to rationalize the denominator!” But why??? Who decided that getting the root out of the denominator and into the numerator was the thing to do?
Here are three reasons why RTD became the standard from Algebra to Calculus.
The Commonsense Reason
The standard reason why you need to RTD is perfectly practical. As you’ve most likely discovered, in mathematics you can often write solutions in multiple different ways and forms. All of these variations are cool, but for practical purposes, they make life more difficult for those grading your papers.
Defining and requiring a standard form for answers saves your teacher the time-consuming headache of having to verify that your solution is equivalent to the answer key, or even worse, accidentally marking your answer incorrect!
Just like reducing a fraction to its simplest form, RTD is the protocol for simplifying fractions with roots in the denominator.
The Reasonable Reason
A commonly defined nomenclature makes sense and all, but still leaves us with the question: why have we decided that having a root in the numerator is okay, but having a root in the denominator is not??
Why is (2 √3) / 3 the simpler form of 2 / √3 ?
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The reason is that if we need to add or subtract fractions with radicals, it’s easier to compute if there are whole numbers in the denominator instead of irrational numbers. For example, it’s easier to add (2√3/3) + (( 3−√2)/7) than the non-rationalized version: (2/√3) +(1 / (3 + √2)).