rationalize-the-denominator-and-write-each-fraction-in-simplest-form-all-variables-represent-posit-9

Question

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.
$\frac{8}{\sqrt{24}}$

Ashley Volpe · Answer

question eight again. We&#x27;re asked to rationalize and simplify. I love to simplify first. So I see this for an eight. So the first thing I&#x27;m gonna do is simplify this down four goes into four once and four goes into eight twice. And so after that simplification, I&#x27;ve got one over to radical six, So it looks simplified, but it&#x27;s not rationalised. So to rationalize, we need to remove this radical six. And we&#x27;re gonna do that by multiplying the numerator and the denominator by radical six multiplying across. We&#x27;re gonna get radical. Six over to now. Radical six times. Radical six is radical. 36 radical 36 of course, is just six. And so we have two times six down here. Which gives us then, of course, radical. Six still on top, in the numerator and on the bottom, we have to time six or 12. This has now been rationalized and simplified

Ashley Volpe · Answer

okay. They want us to rationalize and simplify this. I like to simplify. So radical. 24. I&#x27;m gonna rewrite that as radical for Tom&#x27;s radical six. Um And so what that&#x27;s gonna give me, then, is radical four times radical six over to radical six. Now, that shows me that the top and the bottom have a factor of radical six, so I can remove those that&#x27;s gonna give me radical four over to. Well, radical four is just too, and to over two is gonna simplify down just one.

Ashley Volpe · Answer

all right, We want to rationalize this. We&#x27;re gonna multiply by the con jacket. Square root of Z Moniz eight. We&#x27;re gonna do that on the top and the bottom. Now, that&#x27;s gonna give us distributive on top, so we&#x27;re gonna have four. Oh, radicals E minus four times eight is 32 on the bottom. If we foil this, we get radicals, eat times, radicals e get monness eight radicals E We get positive. Eight radicals E and we get negative 64. Now, if you&#x27;re looking at this, these are gonna cancel out. And so what are we going to be left with for radicals? E Moniz 32 over Z, ma honest. 64 on. There is nothing else I could do to simplify that. So I&#x27;m done.

Ashley Volpe · Answer

question five, We&#x27;re going to you take this expression in rationalize and simplify it. So to do this, we want to remove this radical too. That&#x27;s how we rationalize. And we&#x27;re gonna do that by multiplying the numerator and the denominator by radical, too. When we do that, the top is gonna become four radical, too. And the bottom is gonna be radical two times to just for work. Radical four is just too now looking at that, I can notice that four. And that too. So I&#x27;m gonna simplify now to goes into four twice that it goes into 4 to 2 once and that&#x27;s going to give me then too radical, too over one. And since we&#x27;re over one, we don&#x27;t really need that and said Too radical, too becomes are rationalised and simplified. Answer

Ashley Volpe · Answer

they were asked to simplify and rationalize this expression. I&#x27;m gonna simplify first just because I like I don&#x27;t want to multiply by radical 27. So radical 27 is actually going to simplify down to radical, uh, nine times radical three and radical nine is three. So I&#x27;m gonna rational a simplify radical 27 to 3. Radical three Now, what that gives me then, of course, is 12 on top and three radical three on the bottom. Now 12/3. I recognize will reduce as well to 4/1. So now I have 12 over. Radical three. Just to rationalize this, I need to multiply the numerator and the denominator by radical three. And so that&#x27;s gonna give me then 12 Radical three over three, because radical three times radical three is radical. Non with Jacob&#x27;s three. So now, looking at this, I could actually simplify again because 12 will reduce over 3 to 4/1. And so my final answer, then, is gonna be four radical three over one, which I really don&#x27;t need that one. So my final answer then is gonna be full radical. Three

Problem

Rationalize the denominator and write each fracti…

Problem 11 Medium Difficulty

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.
$\frac{8}{\sqrt{24}}$

Answer

$\frac{2 \sqrt{6}}{3}$

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Algebra 2 and Trigonometry

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Algebra 2 and Trigonometry

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$\frac{2 \sqrt{6}}{3}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry