7-4-51 rationalizing the denominator
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When rationalizing the denominator, we need to realize
that the index is 4, so we need to have four of everything
before we can take one of them out.
So if I think about 25 is 5 * 5, I have two fives right now.
So I need to multiply by two more fives so that I have a
multiplication of 5555 S 4 fives.
I have a single X, so I need three more XS.
So I have a multiplication of a total of four XS or X to the
4th.
But if I do the bottom, I have to do the top by the exact same
thing.
So now we're going to get 4th root.
We multiply inside the radicals, so 3 * 5 * 5 is 25 X cubed Y to
the 7th over the 4th root of five to the 4th, X to the 4th,
and then the 4th root of 5 to the 4th is five, and the 4th
root of X to the 4th is X.
Now this 4th root in the numerator, we don't have 4
threes.
We don't have 4 fives.
We only had five times five.
We don't have 4X's, but we do have more than four YS.
So we're going to think about this.
Four goes into 7/1 full time.
The full time is going to come on the outside with three
leftover.