How do you rationalize this: 1/√π? I think its impossible..??? prove me wrong?

Question

Ok I realized from a previous question that √π/π would still be wrong because pi is irrational and by rationalizing you have to get rid of pi or something like simplify it. Can someone plz show me how to do it and the final most simplified answer.. that would be great.. and try to plz explain in comprehendable 14 - year old math language. thnx a bunch!

Answer 1

Like I said earlier, you can't write 1/sqrt pi in such a way as to have only an integer number in the denominator. The best you could do is write the denominator as an infinte sum such as 4(1- 1/3 + 1/5 - 1/7 + ...)
I figured this was a trick question so I looked up the definition of "rationalise the denominator". It means to write the fraction so that the denominator is an integer. It does not mean to write the fraction so that the numerator is rational or an integer, this is why (sqrt 3)/3 is an acceptable rationalised form of 1/sqrt 3 but you cannot write 1/sqrt pi in a similar form because pi is not an algebraic number.
http://www.webster.com/dictionary/rationalize
You could write this in summation notation (as you'll find in the link I provided last time someone asked this, a little while ago) but you can't simplify it much because it is an infinite sum. Any attempt at "simplifying" it would just make it more complicated!
Your question is a very old one, the ancient Greeks called it the quesiton of squaring the circle. No one could ever do it, but it wasn't till the 15th century that it was proven that it couldn't be done. However, in the quest to square the circle, a lot of good math was discovered about conic sections, etc.
Read the wikipedia link I gave you last time you asked this question, for more info on squaring the circle.

Answer 2

You have two things going on, the radical, which is irrational, and PI itself, which is also irrational. Therefore, the best you can do is eliminate the radical in the denominator by rationalizing the denominator. However, you are left with the irrational PI; therefore, you have not rationalized the denominator at all. You merely reduced the irrationality of the denominator. PI is treated like a number by some, but they are wrong becausee we can only estimate the value of PI, we have no way to know its absolute true value so if you treated it like a number that is not a true answer but merely an approximation, the true answer is an irrational one.

Answer 3

Rationalize USUALLY means get rid of the square root in the denominator, so you could turn 1/√π into (√π)/π, but you're right, this hardly makes the whole expression rational. But then, when you turn 2/√3 into (2√3)/3, the expression STILL isn't rational, it's just that the denominator is a nice integer.

Proving π is irrational takes WAY more math than either you or I know.

Answer 4

You cannot. Pi is irrational, so it's square root must be too, and just taking the reciprocal does nothing to that. Manipulation of the form does not change whether or not it is irrational, it still has the same value.

I don't quite know what you mean by 14 year old math language lol (I just turned 16)... To me that says don't go beyond basic calculus, but that's not true for most people.

If you dont understand something (I didn't fully explain it, but I can if you need me to), just send me a message.

Answer 5

I think that the only goal of this problem is to remove the square roots from the denominator. Otherwise, you are right, pi is irrational and can not be rationalized.

Answer 6

Pi is a number.....

therefore its like any other division problem...
Radical Pi is roughly 1.77

so its like dividing 1/1.77

I dont know if that helped. Maybe I dont understand your question :/

Answer 7

I wish I could, but I don't have the education to. :-)