Algebra
posted by Paula
True or False and please explain so that I can understand.
1. The rationalized form of 125 over the square root of 14 involves no radicals.
2. The radical square root of 4 cannot be used to rationalize the denominator of any radical number.

Reiny
1.
125/√14
= 125/√14 * √14/√14
= 125√14/14 , mmmhhh?
2.
True for √(any perfect square)
If I multiply something by √4/√4 or 2/2
I would simply be doubling the denominator (and the numerator)
So if the denominator contained a radical, doubling it does not make it real
( if √a is irrational, then 2√a is also irrational)
If the denominator had been √4 to begin with, then it would have been a real number anyway , and there would not have been any reason to rationalize it.
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