rationalize-the-denominator-and-write-each-fraction-in-simplest-form-all-variables-represent-posit-3

Question

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.
$\frac{4}{\sqrt{2}}$

Ashley Volpe · Answer

so in question 12 were asked to rationalize and simplify. I like to simplify first. So two and four is going to reduce the one and two. So that&#x27;s gonna give me radical, too over to radical three. To rationalize this, I need to remove that radical from the denominator. And we do that by multiplying by it. And so when we multiply this problem across the top radical two times, radical three is radical. Six and on the bottom, we&#x27;re gonna get to times radical. Nine. Now radical. None is just three. And so this is to Tom&#x27;s three in the denominator. So our answer, then is gonna be radical. Six on top are in the numerator over to Tom&#x27;s three, which is six in the denominator. Final answer. Radical 6/6.

Ashley Volpe · Answer

and ask us to rationalize and simplify. So to rationalize, we gotta remove this radical three from the denominator. And we can do that by multiplying the top and the bottom by that radical. And so we&#x27;re gonna mult by the numerator and the denominator by radical three. On the top, we get four radical three on the bottom. The two was just gonna come across and then we can multiply the two radicals together. Radical three times Radical. Three is radical. None. Okay, on the bottom, we can simplify. We know that radical non is just three. And so on the top we get four radical three on the bottom. We have two and a three with two. Tom&#x27;s three. So on the bottom, we have six. So now it&#x27;s rationalized, but we need to simplify it. Four and six can be simplified to goes into four twice to goes into 63 times. And so our final answer then will be to radical three over three

Ashley Volpe · Answer

all right. If we want to rationalize this, we&#x27;re going to multiply by the conjugal. Do tell the top and the bottom in the numerator and the denominator. And on the top, this is gonna give me distributive property. Well, radical eight times radical A is just a and then radical a comes to is too radical a on the bottom. When we multiply here, we get a because radical eight times radical A is a We get a positive to radical A We get a negative to radical A and the negative two tons positive two is negative, for the only thing I can see to cross out or cancel was gonna be this positive to in this negative tube. And so, what are we gonna get for an answer is gonna be a plus to radical a over and then in our denominator because we cancelled out that intern out her term, were simply gonna be left with a Monness four. And so that&#x27;s gonna be our final answer.

Ashley Volpe · Answer

they want us to rationalize and simplify. We noticed we have a binomial in our denominator, so we&#x27;re going to multiply. By the contrary, it we&#x27;re gonna do that in the numerator and in the denominator that&#x27;s gonna give me a distributive property on the top. So I&#x27;m gonna have radical two times two, which is too radical, too. And I&#x27;m gonna have radical two times radical to which is radical Four in the denominator. That&#x27;s gonna be a using a foil property. So two times two is four. I&#x27;m gonna have positive. Too radical, too. I&#x27;m gonna Negative. Too radical, too. And I&#x27;m gonna have negative radical for cleaning any of this up, simplifying anything I can, um, in the top. I know radical four is just too. I know that two and two or that&#x27;s gonna cancel. Positive. Negative. Radical four is too. So, in the bottom, I get for worm honest too. So what does this look like? Now that we&#x27;ve done some simplification, we&#x27;re gonna end up with too radical, too to radical two plus two over to Well, if you notice that there&#x27;s a lot of twos in that and so we can cross simplify and divide out so to To and to those we&#x27;re all gonna goto ones. And since I have a denominator of one, I&#x27;m not really gonna have a denominator too, right? But I am gonna have a numerator. That numerator is going to be radical too. Waas one.

Ashley Volpe · Answer

So we&#x27;re gonna rationalize and simplify this. And I noticed that the denominator has it by no meal. So we&#x27;re gonna multiply by the conjugated now in the numerator. We also have a binomial, so we&#x27;re actually gonna have to foil the top and the bottom. So we have two terms. Three with just six, we have two times radical too. We have three times radical too. And we have radical two times radical to which we know will just give us, too. On the bottom, we have three times three, which is nine if three times radical too. The native three radical, too. And then we have negative radical to Tom&#x27;s positive radical tea, which will just give us negative right to now we need to do some cleaning up, so I know that we can cancel those out. They&#x27;re gonna go away on the top, notice that we do have some light terms, and so we want to make sure we combine those like terms. So our answer. Then on the top, we have six plus two, which is eight, and we have to radical two plus three radical, too. So we combine those like terms we get by radical, too, and then in the denominator. Since we cancelled out those two terms in the middle, we just have non minus two, which is seven. And there&#x27;s our phone lancer.

Problem

Rationalize the denominator and write each fracti…

Problem 5 Easy Difficulty

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.
$\frac{4}{\sqrt{2}}$

Answer

$2 \sqrt{2}$

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Algebra 2 and Trigonometry

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Ann Xavier Gantert

Algebra 2 and Trigonometry

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$2 \sqrt{2}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry