rationalize-the-denominator-and-write-each-fraction-in-simplest-form-all-variables-represent-posi-22

Question

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.
$\frac{6}{3+\sqrt{3}}$

M S · Accepted Answer

So we have six over three plus describe it of three. So I noticed that we have this radical in our denominator and we cannot have that, so we need to get rid of it. The only way to do that is the multiply the top and bottom by the denominator is conjugated, so the contract is whenever you have a and in this case, plus B, so the consequence of this would be a minus B. So whenever you Foyle, you&#x27;ll get a squared minus B squared. It&#x27;s just easier You have memorized this formula. So confidence are common handy whenever we have a radical in our denominator, because it will help us get rid of that. Because, as you see B will be squared. So most part, it&#x27;s hard bottom by three minus through three cause you have to change the sign. So it&#x27;s simple. Find still have six times three, minus 33 on top and on the bottom with her three squared minus. And then Route three squared someone to go ahead and distribute this six on the top, so have 18 run a six Route three and on the bottom will have nine minus three So if we support for the bottom where six panic we divine are denominator and see larger numbers are enumerating, hating. Devoted my specs. This thing and negative six divided by six gives us negative one, but we&#x27;ll have to write that one there. We&#x27;ll just have negative square three.

Ashley Volpe · Answer

Okay, so we&#x27;ll basically have an expression where we&#x27;re taking two fractions and subtracting them. And so if we want to rationalize them, we&#x27;re gonna rationalize each fraction individually, this one has a binomial. So I&#x27;m gonna multiply by the contra git, top and bottom. This one just has a radical. So I could most about that radical top and bottom. And so what we get when we do that? So on this one, we&#x27;re going to get radical X minus six over. Now, if we&#x27;ve been doing a lot of these this far, we know radical X times radical X is X. We also know that when we do the innards and the outers, they&#x27;re gonna cancel cause we&#x27;re gonna get negative. Six Radical X and positive six. Radical X. So we must we just leave it out. And then, of course, six months. Six. Makes that negative. 36 For this one. We&#x27;re gonna end up with two radical six over six, and we need to recognize that two and six will cancel or reduce. I should say, not cancelled. Um, and so we can make that a little cleaner. And so we should have radical X minus six over X minus 36 minus radical six. Anger three. There you go.

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

question three gives us the expression one over radical three and it ask us to simplify this and write and simplest form. If we&#x27;re going to rationalize this, we have to remove this radical three. So to do that, we&#x27;re gonna multiple the numerator and the denominator by radical three. When we do that on the top, we get radical three and on the bottom, we get radical, non and so radical. Non is three and we have radical 3/3 at the end.

Ashley Volpe · Answer

her. It&#x27;s over this question. We&#x27;re gonna rationalize and simplify. I noticed that my denominator has about no meal. And so to rationalize it, I&#x27;m gonna multiply by its kontic it. And so the Kontic it looks exactly the same, except that it&#x27;s gonna be the opposite sign in the middle. So we&#x27;re gonna multiply about three plus radical three for this problem. Now on top, What we get is distributive. So we&#x27;re gonna do four times three with just 12. And there were 84 times radical three to get four. Radical three on the bottom. We have a binomial times about no meals, so we&#x27;re gonna foil three times three is none. Three times radical. Three is three radical, three negative radical. Three times three is negative. Three radical three. And then we have negative radical three times Radical three to give us a negative radical non. So now that we&#x27;ve done that multiplication, let&#x27;s look and see. Is there anything else going on that we can deal with and so I can see that positive three radical three negative radical. Three radical. Three will cancel out. I know radical non is three. And so on my bottom here on my denominator. I have none on this three. So moving forward from that, what do we get? Her top is gonna be 12 plus four radical three. And the denominator nine minus three is gonna be six. So I&#x27;ve done the rationalization, and I just need to make sure I&#x27;m simplified. My brain immediately shows me I&#x27;ve got 12 4 and six those air all divisible by two. So I&#x27;m gonna divide them all by two to simplify this question. So, what is that gonna give me that&#x27;s gonna give me six plus two Radical three over three. That is gonna be my answer.

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.

Problem

Rationalize the denominator and write each fracti…

Problem 24 Hard Difficulty

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.
$\frac{6}{3+\sqrt{3}}$

Answer

$3-\sqrt{3}$

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Algebra 2 and Trigonometry

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$3-\sqrt{3}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry