Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Irrational Number Raised To Rational Power

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

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Irrational Number Raised To Rational Power

Oh come on you can do this.

Eg root2 squared. Now find another.

B

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Irrational Number Raised To Rational Power

Oh come on you can do this.

Eg root2 squared. Now find another.

B

Now I feel silly. Yes, I can definitely do this. I will return to show my work later after my job interview. Bob, I have a huge decision to make today.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Irrational Number Raised To Rational Power

Good luck!

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Irrational Number Raised To Rational Power

Good luck!

Bob

Thanks. I got the job but it's a standing post.

Anyway, returning to math, here are three more sample problems.

3 Samples:

sqrt{3}^(2) = rational number.

e^(9) = rational number.

(Pi)^(7) = rational number.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Irrational Number Raised To Rational Power

First is OK.

I cannot prove but I think it highly unlikely that powers of e and pi are rational

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Irrational Number Raised To Rational Power

First is OK.

I cannot prove but I think it highly unlikely that powers of e and pi are rational

Bob

What's wrong with the other two?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Irrational Number Raised To Rational Power

I think both result in an irrational. There are easier examples which are definitely rational.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Irrational Number Raised To Rational Power

I think both result in an irrational. There are easier examples which are definitely rational.

Bob

Can you share a few examples?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Irrational Number Raised To Rational Power

See post 2.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Irrational Number Raised To Rational Power

See post 2.

Bob

Copy. We return to regular math tomorrow.