00:02
Okay, so for a statement to be false, right? if a statement is false, all that means is that there's at least one case where it's false.
00:14
At least one case where it's false.
00:19
Where it's false.
00:22
Right? that's what it means to be false in mathematical.
00:25
It doesn't mean that it's always false.
00:27
It just means that there's at least one case where it's false.
00:30
Okay, so let's think about all these.
00:32
A number that is the square of, an integer so if i have an integer in and i square it then it's a perfect square well that's the definition so that is true okay now let's look at the next one a radical of index in is simplified when it's radicand has no factors other than that are perfect nth powers right now let's look at the next one a number is a perfect cube if it is the cube of an integer so i'm just going to go as that and say if i have an integer and it's cubed then it's a perfect cube check that one is that the definition of a perfect cube.
01:05
Perfect nth powers have exponents that are divisible by n.
01:10
So if i have a power, right? so if i have a number, let's just say x, and it says to the nth power, then perfect nth powers have exponents that are divisible by n.
01:21
Right.
01:22
So that means that i have not just x to the n, but x to the k in...