in-3-29-write-each-quotient-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-non-27

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. 
$$
\frac{\sqrt{64 x^{4}}+\sqrt[4]{40 x^{6}}}{\sqrt[4]{x^{6}}}
$$

Matt Gibson · Accepted 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

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

Matt Gibson · Answer

when I want to simplify this problem, first thing I&#x27;m going to do is write it as a fraction. I just think it&#x27;s easier. Look at it that way. Since they&#x27;re both radicals, this is the same as having one big radical of a fraction, so that so Now I can simplify what&#x27;s inside. Six goes into 24 4 times I have the square root of four, which gives me.

M S · Answer

So we want to simplify this expression. So because I have the same radical, we can combine the radical so huh, Q through, Ah, 24 time sub. You square over three, some Soviet to the fourth power. So the regular numbers, we can divide them by the greatest common factor in this case, it&#x27;s three. So 24 divide of our three gives us eight and three. Divide about three. Gives us boy. So we have to queue. Pru? Uh, eights. All right. On top of eight time study. Swear over W to the fourth power. So if you can remember, whenever we I have the same base, would you connects planets they were dividing? We&#x27;re going to subtract those x bunnies. So this is really here, Bruno, eh? Fines w see the second power minus sport. And this gives us a cube root of eight time. Still view to the negative, too, and we don&#x27;t want a negative x one it. So we have the Q group, uh, eight over w Slayer. So because the cube root of eight simplifies to two, if we split apart our top and bottom, we would have ah radical in our denominator and we do not want a rappelling are nominated someone against in the next page. So we left off with the cube root Uh, eight over. Nobody use player so our top will simplify, but our bottom will not. So we need to get our bottom. So you have a exponents of three so that we can get that to counsel out with our radical. So I&#x27;m just gonna multiply the top and bottom by w because, remember, whatever we have the same base with different exponents, we can add those exponents. So this is really exiting a plus B for most part of top and bottom by record there. Don&#x27;t you do it because they haven&#x27;t exploited? Avoid into place. One would have will give us three. So have to queue. Pru Uh, eight w over W 22 plus one Now give us a cube root Uh, a w over W two so you can simplify this further. We&#x27;ll have to queue Brew, huh? A w o ver tu que group? Don&#x27;t be cute. And this cube and his cute girl counsel on the bottom and on top. Thank you, Brit of aids too. So we have two times two group of W over, don&#x27;t we? And this is far as we can simplify that you might think that we can combine W&#x27;s, but we cannot, because one is a we w does not have a radical at all. So they&#x27;re Susan&#x27;s just are finally.

M S · Answer

So we have to skirt a 48 plus spirit of three all over two square three. So the first thing I&#x27;m going to do it I&#x27;m going to separate these into two different factions. So the square root of 48 over the square root of three classes buried in three over this weird of three. So I&#x27;m gonna combine the Prince Fraction Thio the same radical. So 48 everything. And the 2nd 1 this great. They were council with this square to three. So we&#x27;re left with one several reverse tracked. The first radical we know that the greatest coming back there here is three someone to buy cloche model My three. So 48 divided by three gives us 16 in three divided by three years. This void so have the spirit of 16. Most boring. And the square to 16 is for and then bring down plus one and four plus one gives us five

Problem

The area of a rectangle is 25$\sqrt{35}$ square f…

Problem 29 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.
$$
\frac{\sqrt{64 x^{4}}+\sqrt[4]{40 x^{6}}}{\sqrt[4]{x^{6}}}
$$

Answer

$\frac{8+\sqrt[4]{40 x^{2}}}{\sqrt{x}}$

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Algebra 2 and Trigonometry

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$\frac{8+\sqrt[4]{40 x^{2}}}{\sqrt{x}}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry