Prove that 5^(2/3) is irrational

  • #1

Homework Statement


Prove that 5^(2/3) is irrational

Homework Equations





The Attempt at a Solution



I tried writing a proof but that is not getting me any where.

This is what I did so far -

Show that 52/3 is irrational

Proof: Suppose that 52/3 is rational:
52/3 = a/b
52/33/2 = a3/2/b3/2
5(b3/2) = a3/2
Substitute a = 2n + 1, b = 2m + 1;

I don't know if I'm suppose to do like this?
 

Answers and Replies

  • #2
34,309
5,948

Homework Statement


Prove that 5^(2/3) is irrational

Homework Equations





The Attempt at a Solution



I tried writing a proof but that is not getting me any where.

This is what I did so far -

Show that 52/3 is irrational

Proof: Suppose that 52/3 is rational:
52/3 = a/b
52/3 3/2 = a3/2/b3/2
5(b3/2) = a3/2
Substitute a = 2n + 1, b = 2m + 1;

I don't know if I'm suppose to do like this?
It might be simpler to use the fact that 52/3 = ##\sqrt[3]{25}##
 
  • #3
It might be simpler to use the fact that 52/3 = ##\sqrt[3]{25}##
:approve:
Gracias
 
  • #4
34,309
5,948
De nada
 

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