00:01
This problem, we're being asked to rationalize the denominator.
00:03
And essentially, what that means is in our final answer, we cannot have a square root in the denominator of our fraction.
00:09
Well, because we currently have a complex number in our denominator, to get rid of it or to rationalize it, we're going to multiply by its complex conjugate.
00:18
And the complex conjugate of root 2 plus root 5 is going to be root 2 minus root 5.
00:24
So again, we'll multiply the numerator and denominator by.
00:28
So in the numerator, essentially, we're going to distribute.
00:31
5 root 5 times root 2 is 5 root 2 and 5 times negative root 5 is negative 5 root 5.
00:40
Now, in the denominator, this is kind of like multiplying binomials.
00:44
We can use the foil method.
00:46
First, we have root 2 times root 2, which is just 2.
00:49
Remember, when you multiply a radical by itself, essentially it cancels out the radical...