rationalizing the denominators
Why do I have to rationalize the denominators?
In AMC( American mathematics contest ) contests I see that they never leave an answers as 2/root3 it will always be 2root3/3, but in SAT math tests they have answers such as 2/root3. What is the rule and meaning for rationalizing the denominators?(Wondering)
Times both sides by the denominator
If I times that fraction by
, I am actually just multiplying by one. But look at what happens:
So the rule is:
For any fraction multiply by to give
For the purpose of your question, this is how you rationalize the denominator., but for a harder example, you may read on.
However, it gets harder if you have something such as:
In this scenario, you have to use the 'difference of two squares' to rationalize, by making the denominator a difference of two squares, which is where . So apply that to the question, where and b=4:
Note the 'difference of two squares' in the denominator? Using the difference of two squares rule above, we can simplify this to: