I know how to prove that the is irrational, and that is irrational. But how does one go about using the tricks involved in the proof on something like proving that is irrational if:
?
Thanks in advance
I know how to prove that the is irrational, and that is irrational. But how does one go about using the tricks involved in the proof on something like proving that is irrational if:
?
Thanks in advance
You can prove this by contradiction. Assume P is rational.
then try squaring the equation
Use the facts that a square of a rational is a rational, and rational number addition and scalar multiplication is closed under the rational field.
Fiddle around with the squared equation and you'll just have to prove is irrational using those tricks you mentioned, which leads to a contradiction (a rational number = an irrational number)
Oh, and thanks for the help Gusbob, I figured out the polynomial that represented the squared version and had no trouble proving the irrationality of 6^(1/2). That was a clever idea to use the square of the sum of the square roots. I hadn't thought of that before, I know I used it once along time ago, but I forgot about it. Thanks for the help.