rationalize-the-denominator-and-write-each-fraction-in-simplest-form-all-variables-represent-posit-2

Question

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.
$\frac{5}{\sqrt{10}}$

M S · Accepted Answer

So you want to write this faction and simplest form. So because we have this radical in the denominator, I&#x27;m going to go ahead and multiply the top and bottom by that radical so we can get rid of it. But so have five routes and on top and square to 10 times greater. 10 will give us too. And I can reduce distraction five cents by dividing the top and bottom by five. So that would become one and not have become too sue her spirit of tin over too.

Ashley Volpe · Answer

all right. So in a rational as this And were to do that by multiplying by the Contra kit. And we do that on the numerator and the denominator. The numerator is also about no meal, so we&#x27;re gonna have to do some boiling radical 10 times Radical 10 is just 10 radical, 10 times negative one is negative radical 10 on again. Negative one times radical. 10 is negative radical 10 and the negative one times negative one is positive. One in the bottom or in the denominator run into the same thing with a foil so radical 10 times radical 10 is 10 radical 10 times negative one is negative. Radical 10th radical, 10 times positive. One is positive radical 10 and positive one times negative One is nice one. Now, when I look at this, I could notice that negative and positive We&#x27;re gonna cross out the top. We have some light terms, so we&#x27;re gonna combine those when we simplify our answer. So in the numerator, what we get then is 10 plus one, which is 11 and we get negative Radical 10 Monets, radical 10. So we&#x27;re subtracting too radical tens in the denominator, we get 10 monos one, which is not. There&#x27;s the answer to the question

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

Ashley Volpe · Answer

they want us to rationalize three over radical five months to this is a binomial. So we&#x27;re gonna multiply by the conjugal it, and we&#x27;re gonna do that in the numerator and the denominator on the top of this problem. Then we get a distributive property. So three times radical five and then three times two is six in the denominator, we&#x27;re gonna have to foil. So we have radical 25 plus two. Radical five. Modest, too radical. And then we have modest two times positive to Omanis for worth right away. I noticed that I have liked terms in that denominator. Positive to negative two. I&#x27;m gonna cancel out. Radical 25 is just five and so on the denominator of this probably have five minus four. What is our answer, then? Gonna look like in the top. We have three radical files, plus six. Since the denominator is gonna be five minus four or one, we really don&#x27;t need that one under there. And so we&#x27;re gonna leave that as our final answer

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.

Problem

Rationalize the denominator and write each fracti…

Problem 4 Easy Difficulty

Rationalize the denominator and write each fraction in simplest form. All variables represent positive numbers.
$\frac{5}{\sqrt{10}}$

Answer

$\frac{\sqrt{10}}{2}$

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$\frac{\sqrt{10}}{2}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry