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Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.$\frac{\sqrt{20 y}}{y \sqrt{5}+1}$

$=\frac{10 y \sqrt{y}-2 \sqrt{5 y}}{5 y^{2}-1}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 7

Rationalizing a Denominator

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

02:11

Rationalize the denominato…

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02:01

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01:53

02:22

01:48

01:46

01:47

00:52

Rationalize each numerator…

so we have skirt of 20. Why, over why Time Skirt five plus would. So because we can never have this radical and our denominator, we need some lights up. I need to get rid of it. The only way to do that is multiplied by its conjugated. So in this case will have a plus B, and it's conjugated will be a minus meat, so it's whenever you use the same terms. But you just changed the sign in the middle. That way, when you boil, you'll have a squared minus B squared. The middle terms just council out, so it's just easier. If you memorize this formula here that would just make your problem solving go by much quicker. Look, multiply the top and bottom by the conjugated we'll have. Why root by minus one over Why Roubaix minus one. So on top of her route? 20 words sometimes. Why Route five minus one. Staying on the bottom. We'll have why root by squared minus one squared. So it's hard. I don't know if I have to distribute yet. Someone's finally tonight as they are and why Rebar Linus one all over they will have y squared times five minus one. So in about him now will give us look our top floor man a stain Route 20. Why terms our route Rod minus one. You're not of honorable. Have five y squared minus one. I'm gonna go ahead and distribute this route 21 so well here. All under one radical 20 y times. Why comes fine? Minus and then Route 20 Wife Oliver five y squared. Run this one. And when it's hot five times 20 gives us 100 and then one times why will give us y squared and then Linus, 20 watts rates when you want all over five y squared minus one and then on top discovery of 100 y squared so you can just take the square root of each of those terms individually. So let's say this square root of 100 gives us 10 in a square root of y square. It gives us why. So have 10 wide runner's Route 20. Why all over five y squared minus one. And that's a CE faras. We can simplify this. So the answer. Who's this part right here?

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