00:01
To rationalize a denominator like this, we multiply by the conjugate.
00:04
We take the same thing that's in the denominator and multiply it by its opposite, meaning 7 plus 5 times a square of 3.
00:10
So now let's go ahead and multiply, and what we do, we have to foil.
00:14
So in the numerator, 4 times 7 is 28.
00:17
4 times 5 gets you plus 20 square root of 3.
00:21
Then the square root of 5 and 7 is plus 7 square root of 5.
00:25
And then when we multiply it times square to 5 times 5 square to 3, will be 5 on the outside, 15 inside.
00:33
And the denominator, though, 7 times 7 is 49...