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

Thread starter trap101
Start date Feb 14, 2012
Tags

Irrational

Click For Summary

The discussion centers on determining the irrationality of the expression (2^1/2 + 7^1/3)^1/2. The user confirms that both 7^1/3 and 2^1/2 are irrational. They initially seek guidance on proving the irrationality of the entire expression but later indicate they have solved the problem independently. The conversation highlights the challenge of proving the irrationality of sums and roots of irrational numbers. Ultimately, the user successfully figures out the solution on their own.

Feb 14, 2012

trap101

Hi,

So I proved that 7^1/3 is irrational, and I know 2^1/2 is irrational, but how can I show if (2^1/2 + 7^1/3)^1/2 is irrational?

Hint of where to start?

Physics news on Phys.org

Feb 14, 2012

trap101

Never mind, figured it out.

Feb 14, 2012

checkitagain

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.

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

View full post »