rationalize-the-denominator-and-write-each-fraction-in-simplest-form-all-variables-represent-posi-12

Question

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.
$\frac{\sqrt{24}}{2 \sqrt{6}}$

M S · Accepted Answer

So we have the square root of 24 over two times as growed of six. So we&#x27;re gonna multiply the top and bottom by this radical and the denominator because we want to get rid of that radical. So we&#x27;ll have scared of six over squared of six. This becomes 24 times Route six over two times six. So instead of multiplying that big number, I&#x27;m going to simplify our 24. So let&#x27;s talk about our factors of 24 we have one. We&#x27;re gonna have one and a two and 12 three and one in 24. Sorry Soon&#x27;s will three and eight in foreign six. So perfect square. I see. Here is this four here. We&#x27;re gonna have scared of four times every six times, Russi all over two times six, which is 12. So on talk, we see two routes sixties. So that&#x27;s gonna turn into six over its well. And we can also simplify our screw before which was turned into two. So have 12 over 12 and I will give us one

Ashley Volpe · Answer

question Number 10 asked me to rationalize and simplify this expression I like to simplify first. So radical 12 is actually radical. Four times radical. Three radical four is too. So we really have six over to radical three six over to can simplify to 3/1. And so I have three over radical three that I need to now rationalize. If I&#x27;m gonna rationalize, I need to remove the radical from the denominator. And so we&#x27;re gonna do that by multiplying the numerator and the denominator by radical three radical three times Radical Three is gonna be radical. Non. And on the top, I&#x27;m gonna have three radical three radical non is just three. And then I noticed the three and three top and bottom are gonna cancel out. And so my final answer then that I&#x27;m gonna be left with It&#x27;s just gonna be radical. Three

Ashley Volpe · Answer

for question 11. We want to rationalize and simplify this. I like to simplify first, So I&#x27;m going to make this into radical four times radical six radical forests to. So this is radical six. So we&#x27;re gonna have eight over to radical six. I can notice that eight and two can be reduced to four and one. So that&#x27;s gonna give us four over. Radical six. If I want to rationalize this, I need to remove that radical from the denominator. And we do that by multiplying the numerator and the denominator by that radical that&#x27;s going to give me a four radical six over radical 36. Radical 36 is just six and 4/6 will reduce to to over three. And so my answer here at the end is going to be too radical. Six over three

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

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

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.

Problem

Rationalize the denominator and write each fracti…

Problem 14 Easy Difficulty

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.
$\frac{\sqrt{24}}{2 \sqrt{6}}$

Answer

1

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