in-3-29-write-each-quotient-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-non-10

Question

In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero. 
$$
\frac{\sqrt{80 x^{2} y}}{\sqrt{30 x y^{2}}}
$$

M S · Accepted Answer

So we have this girl of 80 times x squared. Why? Divided by this group of 30 times X y squared. So purses right this to her one radical. So have a t X squared. Why divided by 30 x y square. So remember, whatever we have the same basis and we&#x27;re dividing, you can combine them by subtracting their exponents. So, for example, first, let&#x27;s reduce our regular numbers here so we can divide them by their degrees. Coming factor. In this case, it&#x27;s Tyg. So 30 divided by 10 gives us three in 80. Divide about 10 gives us eight, so would have eight over three. And also now we can focus on our variables. So we have X squared divided by X. That&#x27;s two minus one and only give us one and then we&#x27;ll have why, And that would be 11 is to give us a negative one. And because we have this negative one and the numerator, we don&#x27;t really want to have negative exponents. We&#x27;re gonna go ahead and move it to the bottom. So I ate it over 31

Matt Gibson · Answer

to simplify this problem. I&#x27;m going to first write it using the division bar. It just makes it easier to understand that way. It&#x27;s the exact same thing. So this would be the same as one giant division or a square root. And I&#x27;m just going to put both inside that same radical. But we simplify next, So this would be the same as the square root Three divides into 24 cents. They&#x27;re both inside the radical that can reduce. So I get this. Where? Route of eight expert in the numerator excuse in the denominator gives me just X. Now I can&#x27;t leave a radical in the denominator, so I need to rationalize this denominator by multiplying the top and bottom by The square root of X. That&#x27;s the same is multiplying it by one. Anything divided by itself gives me is one. So this gives me the square root of that On the top on the denominator, I get the square root of X squared A is a square to 400 square to which I can simplify to be to times the square root of two. So this top to the numerator simplifies to be to times this word of two x the denominator the squared of X squared is just X

M S · Answer

so we have to square root of 300. Divide about this Gordon 25. So first we can write this under one radical. So we have 300. Get out about 25 and just like any other fraction, we going to sit by reducing about the greatest common factor in this case to go was coming factors. 25. That&#x27;s when you find out about 25 gives us one and 300 divided by 25. Gives us 12 so we have to square it. It&#x27;s whoa. They want to see if we can reduce this further. So let&#x27;s write the factors of 12. So we have lines well, two and six and three and four and I see a perfect square here for So now we want to write these radical tohave. The square root of four and four times three gives us 12 times very 23 when we get simplified this story before, too. And then we bring down too scared of three

Matt Gibson · Answer

when I have a binomial divided by a mono meal. I need to divide both terms on top by that my new meal. So I&#x27;m dividing each of these. So I wind up with the numerator, each term divided by the denominator. Plus, because of this plus here, now I can just reduce I can think of this is being one giant Q brute around each one. It&#x27;s the same thing, so I really just reducing what&#x27;s inside the radicals. So I wind up with the cube root of nine, plus the cube root of 12 x squared. I&#x27;m looking for perfect hue brutes. Perfect. You brutes would be like eight and 27. There&#x27;s no perfect you brute in nine. So this would be just the cube root of nine plus 12 doesn&#x27;t have any perfect few birds, either. It doesn&#x27;t have an eight or 27 as a factor. And if x squared has a smaller exponents in the index here, I can&#x27;t do anymore, so this would be my final answer

Matt Gibson · Answer

So to simplify this problem when I have a radical divided by another radical, this is the same as having one big radical with the other two inside, which makes it easy to simplify. I can divide, since they&#x27;re both even 27 has a perfect square. This would be the same is nine times three, so this would be the squared of nine times the square to three, which simplifies to be three times the square root.

M S · Answer

so we have to scrape a 75 divided by the square to three. So the person you want to do is I&#x27;m gonna separate the we&#x27;re actually gonna write as a faction. So spirit of 75 divided by a spirit of three. And I want to split apart Thescore to 75. So I noticed that we have a three and already nominated, and I know that he&#x27;s a factory of 75. So let&#x27;s say scared of three times spirit of 25. Well, it it was split apart. That&#x27;s 3 75 and this also divided by the square and a three. So these two terms of cancel out and we&#x27;re left with this great of 25 then we get simplified that down and so but

Problem

In $3-29$ write each quotient in simplest form. V…

Problem 12 Easy Difficulty

In $3-29$ write each quotient in simplest form. Variables in the radicand with an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.
$$
\frac{\sqrt{80 x^{2} y}}{\sqrt{30 x y^{2}}}
$$

Answer

$\sqrt{\frac{8 x}{3 y}}$

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$\sqrt{\frac{8 x}{3 y}}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry