SOLUTION: Can an irrational number raised to an irrational power yield an answer that is rational? This problem shows that the answer is “yes.” (However, if you study the following solut
Algebra.Com
Question 1207368: Can an irrational number raised to an irrational power yield an answer that is rational? This problem shows that the answer is “yes.” (However, if you study the following solution very carefully, you’ll see that even though we’ve answered the question in the affirmative, we’ve not pinpointed the specific case in which an irrational number raised to an irrational power is rational.)
(a) Let A = (sqrt{2})^(sqrt{2}). Now, either A is rational or A is irrational. If A is rational, we are done. Why?
(b) If A is irrational, we are done. Why?
Hint:Consider A^(sqrt{2}).
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.
a soup of words with zero mathematical meaning.
Did I say " . . . with zero mathematical meaning" ?
No. it is not right. It is better to say " with negative mathematical meaning ".
So, it is better to glue up your eyes and ears with adhesive tape
so as not to see or hear this MEGA-gibberish.
RELATED QUESTIONS
Give an exmple in which a rational number raised to a rational power is... (answered by funmath)
Give an example that shows that each of the following can occur.
a. The sum of two... (answered by Alan3354)
Show that the product of a non-zero rational number and an irrational number is an... (answered by ikdeep)
This section is dealing with contradictions.
Show that the product of a non-zero... (answered by ikdeep)
5)Which number can be multiplied to a rational number to explain that the product of a... (answered by hkwu)
Is __________ an irrational or rational number?
0.285714 (answered by checkley77)
Explain why the product of a nonzero rational number and an irrational number is... (answered by solver91311)
2.Explain why the sum of a rational number and an irrational number is... (answered by richard1234)
Why is the product of a non zero rational number and an irrational number irrational... (answered by MathLover1)