- #1
omega16
- 20
- 0
Consider Q[sqrt(2)].
Does every element of Q[sqrt(2)] have a square root in Q[sqrt(2)] ?
Prove if true, and give a counterexample if false.My solution:
sqrt(sqrt(2)) = a + bsqrt(2)
if I square both sides then I will have :
sqrt(2) = (a + b*sqrt(2))^2
= a^2 + 2ab*sqrt(2) + 2b^2
=======================
I think the answer should be false. Am I right?
If I am right. Can you suggest me a counterexample. Thank you very much.
If I am wrong. Please correct me. Thanks
Does every element of Q[sqrt(2)] have a square root in Q[sqrt(2)] ?
Prove if true, and give a counterexample if false.My solution:
sqrt(sqrt(2)) = a + bsqrt(2)
if I square both sides then I will have :
sqrt(2) = (a + b*sqrt(2))^2
= a^2 + 2ab*sqrt(2) + 2b^2
=======================
I think the answer should be false. Am I right?
If I am right. Can you suggest me a counterexample. Thank you very much.
If I am wrong. Please correct me. Thanks