SOLUTION: is there somewhere on the internet where it could help me solve the question? Here is one of the questions it says Remove the radical from the denominator of the following f

Question 175089: is there somewhere on the internet where it could help me solve the question?
Here is one of the questions it says Remove the radical from the denominator of the following fraction without changing the value of the fraction. could you please explain this to me step by step and show me this method with an example?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You are describing a process called "Rationalizing The Denominator" which simply means to convert the fraction so that the denominator is a rational number. The trick is to multiply the fraction by 1 in the form of where is selected so that after the multiplication the denominator is a rational number.

For example, rationalize the denominator of . In order for the denominator to be rational, we need to multiply it by , so that is our value for in this case. The process looks like this:

The process becomes a little more complex when you are faced with a denominator that is in the form where either or (or both, for that matter) is irrational. In this situation, say if we had as a denominator, there is no simple number that we can use as a multiplier to convert this denominator to a rational number.

What you need to do is to recall the "difference of two squares" factorization, namely: . That means you can take something like and multiply by it's conjugate, to arrive at

Let's do an example:

Rationalize:

The conjugate of the denominator is , so we have to multiply the original fraction by 1 in the form of , thus:

You can read more about this at:

http://www.math.unt.edu/mathlab/emathlab/How%20to%20Rationalize%20the%20Denominator%20of%20a%20Fraction.htm

http://www.helpalgebra.com/articles/rationalizedenominator.htm

Or just Google "rationalize the denominator" for a bunch more.
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