Rational & Irrational Numbers

[nycmathguy]

(a) Give an example in which the result of raising a rational number to a rational power is an irrational number.

(b) Give an example in which the result of raising an irrational number to a rational power is a rational number.

 

[MathLover1]

a.
2 is rational number, 1/2 is rational number, and 2^(1/2) =sqrt(2) which is an irrational number

b.
sqrt(2) is an irrational number, 2 is rational number,
(sqrt(2) )^2=2 which is an rational number

 

[nycmathguy]

a.
2 is rational number, 1/2 is rational number, and 2^(1/2) =sqrt(2) which is an irrational number

b.
sqrt(2) is an irrational number, 2 is rational number,
(sqrt(2) )^2=2 which is an rational number

Thank you. I bet you never thought in a million years that you would come across a math fanatic like myself. Right?

 

[HallsofIvy]

A "math fanatic"? Most of the questions you post, with no attempt to solve them yourself, are either arithmetic or basic definitions! This problem is just a matter of knowing the definitions of "rational" and "irrational" numbers.

 

[nycmathguy]

A "math fanatic"? Most of the questions you post, with no attempt to solve them yourself, are either arithmetic or basic definitions! This problem is just a matter of knowing the definitions of "rational" and "irrational" numbers.

I don't just post questions when help is needed. I post math questions for those who are, as you put it, "math fanatic."

 

[HallsofIvy]

"Math fanatic" was your description of yourself. But you are NOT a "math fanatic". You do not even know what mathematics is!

 

[nycmathguy]

Why would you say that to me? I am a math fanatic living a horrible life. Do you know what it means to work 40 overnight hours? Do you know about my physical abnormalities? Do you know about my weekly hospital visits for physical therapy? I gotta squeeze math into my daily life. It's not easy at all.

 

[HallsofIvy]

No, you are not a "math fanatic". You have already told us that you don't like precise language, preferring loose, general statements, the antithesis of mathematics.

 

[nycmathguy]

No, you are not a "math fanatic". You have already told us that you don't like precise language, preferring loose, general statements, the antithesis of mathematics.

A good teacher, professor, or tutor breaks the material down to the level of students. The student must walk away from the lesson knowing that it was not a waste of precious time. During my time as a substitute teacher (8 years), I made it my business to break down the material to the level of students in all the classes that I covered for absent teachers. Many of the students said THANK YOU MR. X (I will not reveal my name in an open forum).

 

[HallsofIvy]

Yes, but being elementary has nothing to do with being precise!
You can break down material while still being precise.

 

[nycmathguy]

Yes, but being elementary has nothing to do with being precise!
You can break down material while still being precise.

Ok. Cool. Let's break down the material in a precise manner.

 

[HallsofIvy]

When you are asking questions about differential equations AND basic algebra it is hard to know how to break down the material!

 

[nycmathguy]

When you are asking questions about differential equations AND basic algebra it is hard to know how to break down the material!

You are right. However, I post questions not only to get help but to give others who love math practice problems to play with.