00:01
So can an irrational number raise to an irrational power be rational? so let's take a look at a case where we have a, which is equal to the square root of two, raise to the square root of two power.
00:16
There are two possible outcomes, either a is rational or a is irrational.
00:22
Well, if a is rational, then we're done.
00:25
Yes, root two raise to the root two power could be some rational number.
00:30
Now for part b, if it's irrational, how does that help us? so this is a small trick.
00:41
Let's say that a is some irrational number, right? so we have a, and let's raise that to the root 2 power.
00:50
That's an irrational number, so we have an irrational number raised to an irrational power...