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Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.$\frac{4}{4+\sqrt{7}}$

$\frac{16-4 \sqrt{7}}{9}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 7

Rationalizing a Denominator

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

02:02

Rationalize the denominato…

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01:25

02:54

02:38

01:09

00:31

01:21

01:39

So we have four over four, plus the square root of seven. So because we have this radical on our denominator, we need to get rid of that. And the only way to do that is so multiply by its conjugated. So congregate is whenever you have two terms in this case, will have a plus B if the most probably the contrary it we need to multiply about those same two terms would change the sign. So whenever way boiled is, we'll get the first term square, minus the seconds for him squared. You could boil it completely, but just note at the middle terms will kill so well because you have a plus and minus. So you just end up with a square minus B squared. So it's just easier if you memorize this formula here. So let it go ahead and well supplied by its conjugated. So we have four minus is great of seven over four, minus the square to someone it's on the top will have fuller from Spore minus 37 over four squared minus route seven. It's weird. So the top of going to go ahead and boil that I'm gonna go ahead and distribute that for four times 4 16 in the now just before seven. On the bottle, four square to 16 and scared of seven square. It will give us seven well 16 minus four, Route seven over nine.

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