in-3-38-write-each-expression-in-simplest-form-variables-in-the-radicand-with-an-even-index-are-no-9

Question

In $3-38$ write each expression 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.
$$
\sqrt{24 x y^{2}}+\sqrt{54 x y^{2}}
$$

Julie Silva · Accepted Answer

we&#x27;re being asked to simplify the given expression. Remember, when you&#x27;re adding radicals, you want to simplify both radicals first. So let&#x27;s start with the first one. We have the square root of 24 x y squared. Well, I can simplify the square of the 24 because the perfect square four goes into 24 6 times. So I&#x27;m going to rewrite this as to square the four times the square, the six. Then I&#x27;m gonna leave X in its own radical and only why square than its own radical. Then I&#x27;ll bring down our plus sign. And now let&#x27;s take a look at our second radical. We have the square of the 54 x Y squared. Well, we can simplify the square of the 54 because the perfect square nine goes into it six times. So I&#x27;ll rewrite this a square The nine Times Square The six again I&#x27;m gonna leave the square root of X in its own and I&#x27;m gonna leave. Why squared in its own radical? All right, so let&#x27;s go ahead and simplify. Well, the square of the forest to and the square of the UAE square is Why now we can&#x27;t simplify the square of the six or the square. The axe. So we&#x27;re gonna leave that together inside the rattle. We&#x27;re going down the plus sign. Now let&#x27;s go to our next set. Well, the square the nine is three. The square of the Y squared is why. And again we can&#x27;t simplify the square of the six or the square that X So we&#x27;ll rewrite that in one radical. Okay, Perfect. Now both radicals, air simplified. And these two terms of like terms because both radicals have the same Radha can. So we simply need to combine the coefficients well, two y plus three y is five y. So we&#x27;ll bring down five y and then we&#x27;ll bring down our radical the square of the six X. So now we&#x27;ve simplified our expression. So our final answer is five y times the square root of six X

Julie Silva · Answer

we&#x27;re being asked to simplify the given expression. So the first thing going to do is simplify any radicals. Well, the only radical that could be simplified fervor is this last radical. So I&#x27;m gonna bring down two times two square with three y minus five y squared, plus four times the square of the three. Why? And now let&#x27;s look at this last term. Well, the square the 36 is equal to six or in take out the six. And then we have the square root of y to the fourth, which is just y squared. Okay, great. Now all of our radicals are simplified. Now we want to combine any pairs or like terms. Well, the first parallel terms. We have our tuber three y and four Route three y Well, two plus 46 So that will give us six times the square root of three. Why? Well, our next pair of late terms are negative. Five y squared and positive. Six y squared. Well, negative. Five y squared plus six y squared is just positive y squared. And these terms are not like terms, so we can&#x27;t simplify any forever. So our final answer is six Route three y plus y squared

Finian Lickona · Answer

All right, So for this exercise, we&#x27;re going to be simplifying the expression X Times radical 600 minus two. Radical 24 X squared. Hoo boy plus four x radical 96. Okay, so the first thing we&#x27;re gonna do is try to simplify this radical right here, notice that we can rewrite it a six times 100. 100 is the perfect square of 10. So we&#x27;re just gonna rewrite this as 10 Ex radical six. We can rewrite this 24 as four times six. And this X squared is already a perfect square, so we can factor that out. So if we factor this four outside of the radical we get, I&#x27;m gonna bring that to down times to the ex, gets factored out of the radical, and we are left with a six under the radical plus four X. And then this 96 can be rewritten as six times, actually. What? ISS 96. I swear I&#x27;m gonna math. Okay, anyways, so it&#x27;s not 18. It&#x27;s six times 16. So 16 is obviously a perfect square, and we can factor that outside of the radical as four. So we&#x27;re actually gonna include a times four right there and that six days inside the radical. So we really have Here is 10 x minus four X plus 16 x and they&#x27;re all times radical. Six. And if we simplify this 10 plus 16. 26 minus four is 22. So our final answer is going to be 22. Ex radical six.

Finian Lickona · Answer

So in this exercise, we&#x27;re going to simplify the expression Route 24 plus to route three halves. Now I want to get these radical terms to match. So I&#x27;m going to have to find a way to make this 24 look like a three halves. I can rewrite this 24 as 48 over to and now the denominators of both radical terms match. So what I&#x27;m really going to do is find a way to decompose this 48 into some perfect squares. So I recognize that I can rewrite this as three times 16 over, too. And this 16 right here could be factored out as a four. So what I really have is four times three over route two, plus two times three over route to which, of course, simplifies to six. No times radical. Three over two

Finian Lickona · Answer

So in this exercise, we&#x27;re going to simplifying the expression three X to the third re 80 plus to route 125 x two of sixth. So the first thing I&#x27;m gonna do is try to simplify this radical a little bit more. I see that I can recreate this as five times 16 so I can factor a four out of this radical and put that out in front here. So this is gonna become a 12 x to the third route five. So now I want to see how I can simplify this radical I c. I can rewrite this as that&#x27;s not going to be too as five times 25. And I can rewrite this as X squared times x squared times X squared. So if I factored this fi about that brings a a five outside of the radical on. And then all these X squared terms become one x cubed term outside of the radical, and I am left with a five inside the radical, which is what I wanted. So I have 12 x to the third over Route five and then two times five is 10 x to the third Route five. So our final answer is clearly going to be 22 x to the third Route five

Finian Lickona · Answer

All right, So in this exercise, we&#x27;re going to be simplifying the expression 49 x cubed under a radical minus two. Ex radical for X. So we want to make this radical looks something like this radical. So immediately, we recognize that 49 is a perfect square, it seven times seven and then X cube can be re written as X squared times X. So we can fact with seven out in front of the radical and the X squared out in front of the radical and we are left with just an ex inside of the radical. And now we move on this particular radical term right here. Four is a perfect square, so we can factor that out, is it too? So this term becomes four ex radical. So our secondary simplified stages seven ex radical X minus four x radical X, and this is very easy to solve. So seven minus four means that our final answer simply three ex radical acts

Problem

In $3-38$ write each expression in simplest form.…

Problem 11 Medium Difficulty

In $3-38$ write each expression 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.
$$
\sqrt{24 x y^{2}}+\sqrt{54 x y^{2}}
$$

Answer

5$y \sqrt{6 x}$

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5$y \sqrt{6 x}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry