rationalize-the-denominator-and-write-each-fraction-in-simplest-form-all-variables-represent-posi-24

Question

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

M S · Accepted Answer

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&#x27;s conjugated will be a minus meat, so it&#x27;s whenever you use the same terms. But you just changed the sign in the middle. That way, when you boil, you&#x27;ll have a squared minus B squared. The middle terms just council out, so it&#x27;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&#x27;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&#x27;ll have why root by squared minus one squared. So it&#x27;s hard. I don&#x27;t know if I have to distribute yet. Someone&#x27;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&#x27;re not of honorable. Have five y squared minus one. I&#x27;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&#x27;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&#x27;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&#x27;s Route 20. Why all over five y squared minus one. And that&#x27;s a CE faras. We can simplify this. So the answer. Who&#x27;s this part right here?

Ashley Volpe · Answer

all right. So they want me to rationalize this and I see about no meal. So I&#x27;m gonna multiply about con jacket and since I&#x27;m gonna multiply the denominator also gonna multiply the numerator. The numerator here is already about no meal, so I&#x27;m gonna have to foil this problem. So first to radical X times radical X is just gonna be two x two radical x times Negative radical y is going to be negative, too radical. And then you can just put the X and the Y under the same radical sign inner side. We&#x27;re gonna have negative five And then again, that radical X y and then your last terms. You have a negative times a negative, which makes positive, and you have a five and then you have radical wide times radical. Why? Which makes just simply a while when you do that last one There in the denominator we have radical X times radical X, which is just X. We have radical X times with radical y. So that&#x27;s negative Radical X y, inside x and y So that&#x27;s positive Radical X y. And at the end we have a positive and a negative. We have radical wide times radical. Why? Which is just why I noticed these air going to cancel. And then I see here that I have some light terms, So I wanna make sure I combine those in my final answer. So in the numerator, we&#x27;re gonna have to x What? That was to us. We have modest two and minus five, so that&#x27;s minus seven Radical X Y, and then plus five wide the end in the denominator. Since those inner and outer terms canceled, then all we&#x27;re left within our denominator is X minus y. There is our final answer to this question.

Ashley Volpe · Answer

question for Ask us to rationalize and simplify five over radical 10. To do that, what I&#x27;m gonna need to do is multiply at the top and the bottom by radical 10. On the top of this problem, that&#x27;s going to give me five times radical. 10. Think and on the bottom I&#x27;m going to get the radical of Tin Toms 10 which is radical. 105 radical 10 radical to 100 is simply 10. Oh, and then I have to remember that I can cross our simplify these so far I will go into five once and it&#x27;ll go into 10 twice so I can actually reduce that fraction down to get a final answer then of radical 10 over t.

Ashley Volpe · Answer

question 16. Ask us to rationalize and simplify. We have a bond, no meal in our denominator. So we need to multiply by the contra git and the contra get again is the exact same things that we change the sun in the middle of it. So instead of being five monness radical to we&#x27;re gonna do five plus radical, too on the top, we&#x27;re just gonna multiply straight across. And so we&#x27;re going to get five plus radical, too. On the bottom, we&#x27;re gonna have to use our foil. So we&#x27;re gonna do five times five. We&#x27;re just 25. We&#x27;re gonna do five times radical, too. We&#x27;re gonna do negative radical two times five and then we&#x27;re gonna do negative radical to Tom&#x27;s positive radical, too, for a negative radical four. Now we&#x27;re gonna look at it and see if there&#x27;s what can we do? What can we do to simplify this? Well, I noticed that there&#x27;s a positive five radical two and a negative five radical team. Those were going to cancel out radical four is just too, and so on the bottom. Here, we really only have 25 Moniz to so to finish our problem then we&#x27;re gonna rewrite top part of this. We&#x27;re gonna get by, plus radical, too, over 25 months to which is 23. And so our final answer in this question is gonna be five. Radical, too. Are five plus radical to sorry. Over 23.

Ashley Volpe · Answer

rationalize and simplify this. And I like to simplify first and recognize five and 15 as reducing to one and three. So we currently then have the radical 500. And in the numerator and in the denominator, we have three radical, too. To rationalize this, we&#x27;re gonna multiply by that radical that&#x27;s in the denominator. We do that on the numerator and the denominator. So that&#x27;s going to give me on top radical five times radical to which is radical 10. And on the bottom, I&#x27;m gonna get three radical four. Well, radical four is just too. And so this becomes three times to on the denominator side. And so when I do that, my final answer then will be radical 10 over six.

Ashley Volpe · Answer

they want us to rationalize and simplify So we&#x27;re gonna multiply. We noticed this binomial. So we&#x27;re gonna have to you multiply by the conjugated We&#x27;re gonna do that in the numerator and in the denominator on the top, we&#x27;re gonna end up with the distributive property. Now, hopefully is you&#x27;ve been going through these problems were starting to recognize that if you multiply our radical by itself, you actually end up with what&#x27;s underneath that radical so radical five x times radical five X is actually just five X and then we&#x27;re gonna do radical five x times two In the denominator, this becomes the foil property. So we&#x27;re gonna most by radical five x times radical five x, which will just give us biotics. We&#x27;ve got a positive to radical politics. We&#x27;ve got a negative to radical five X and then we have negative two times two, which is negative for work. Your inner and outer terms here positive to negative two will cancel. And so you&#x27;ve got five X minus four in the denominator. So nothing else I can see is gonna simplify in this case. So let&#x27;s rewrite our answer. So our final answer and this question is going to be five x plus two radical five x over five eggs minus four

Problem

Rationalize the denominator and write each fracti…

Problem 26 Hard Difficulty

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

Answer

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

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry