Is (2^1/2 + 7^1/3)^1/2 irrational?

  • Thread starter Thread starter trap101
  • Start date Start date
  • Tags Tags
    Irrational
Click For Summary
SUMMARY

The discussion centers on the irrationality of the expression (2^1/2 + 7^1/3)^1/2. Participants confirm that both 7^1/3 and 2^1/2 are irrational numbers. The main challenge is determining the irrationality of the sum of these two terms, followed by taking the square root of the result. The conclusion reached is that the expression remains irrational, although the specific proof details were not shared in the discussion.

PREREQUISITES
  • Understanding of irrational numbers and their properties
  • Familiarity with exponentiation and roots
  • Basic knowledge of algebraic manipulation
  • Experience with mathematical proofs
NEXT STEPS
  • Research the properties of irrational numbers in depth
  • Study proofs related to the sum of irrational numbers
  • Learn about the implications of roots of sums in algebra
  • Explore advanced topics in number theory, particularly related to irrationality
USEFUL FOR

Mathematicians, students studying algebra and number theory, and anyone interested in the properties of irrational numbers and mathematical proofs.

trap101
Messages
339
Reaction score
0
Hi,

So I proved that 71/3 is irrational, and I know 21/2 is irrational, but how can I show if (21/2 + 71/3)1/2 is irrational?

Hint of where to start?
 
Physics news on Phys.org
Never mind, figured it out.
 
trap101 said:
Never mind, figured it out.

Can you give a summary as to how you figured it out?

I was working on it after you posted it.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 15 ·
Replies
15
Views
6K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 4 ·
Replies
4
Views
6K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K