in-3-38-write-each-radical-in-simplest-radical-form-variables-in-the-radicand-of-an-even-index-are-7

Question

In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.
$$
5 \sqrt{200 x y^{2}}
$$

Finian Lickona · Accepted Answer

So for this exercise, we want to simplify five radical 200 x y squared. So if we decompose the 200 term into squares, a product of some number in a square, we can write it as two times 100. And then the Y squared, of course, is simply why squared so we can bring that out in front of the radical as a whiter. Have five down here, bring that expect. And then, of course, the square root of 100 is 10. So we can cross that off and included 10 out here. So our final answer is going to be 50. Why? Route to X.

Nick Johnson · Answer

five times the square root of 200 x y squared Well realized that 200 right? Well, that is two times a perfect square day. Me two times. 100. You can go ahead and rewrite this as five times. The square root of that stuff is 200. This could be 100 times two. Right? Then, while times acts times, why squared? But then we can go ahead and weigh. Have now Ah, product here. Right in our square root. We can separate this as five times, while the square root of 100 it times well, the square root of two times the square roots off acts times the square root of why squared, right? Um but then we can then go ahead and take the square of 100 which is a perfect square, right? It&#x27;s quite a 110. So we pull a 10 out five times 10 which is 50 and then we still have, or a square 22 and a square root of X. Okay, this is the square root of two X that can&#x27;t be simplified any further. But then a square with a why square or is why So the why I can then come out 50. Why? On which left out of the square root would be, well square root of two times quarterbacks, which is a square room off to axe. All right, so there we have it.

Finian Lickona · Answer

all right. So for this exercise, we want to write the term three times the square root of 20 wide of the fifth. And it&#x27;s most simple radical form. So let&#x27;s think about ways in which we can decompose the 20 term into square term. So 20 is four times five when we recognize that four is a perfect square, and then the white of the fifth term can be rewritten as wide of the fifth. No, I&#x27;m sorry. Why squared times y squared times? Why, Due to the law of addition of exponents So and we&#x27;ll bring that three down so we can take this four out of the radical and it becomes a two. We can take this y squared out and this y squared outs that&#x27;s too wise that get brought out of the radical. So it&#x27;s gonna be White Times. Why? Which is why squared and we are left with a five and a single white term still under the radical. So our final answer is six y squared Route five wine

Nick Johnson · Answer

the square root of X over five y cube. Okay, this is equal to the square root of eight at eight. Axe AIDS X over the square root of five. Why pube? Okay, what a squirt of eight X. That&#x27;s the squared of eight times. The square root of X squared of aid can be rewritten as a square root of four times two right times the square root of acts over while the square root of five y cube, I guess way written as the square root of wealth. Five. Why, um, we&#x27;re both five y square times. Why, Okay, that&#x27;s his five wise cube. But then, well, the squirt of four times two is quit of four times square to two, so the squid of four is too. So screwed of eight is equal to two times the square root of two. Because you have a product under your square root, you can go ahead and take the square root of a perfect square that can come outside of your radical, so the square root of four is too, so we&#x27;re left with two times the square root of two. But then times the squirt of X. That&#x27;s two times the square root of two X. And I know that this is equal to the square root of X. It&#x27;s good of it. X is the square root of four times two times acts, so that&#x27;s equal to two times the square root of two X. Okay, Divided by Well, uh, there&#x27;s not much you can do here except for taking the square root of why square is just why. So that could come out. We have. Why times the square root of five wine. All right, all right.

Finian Lickona · Answer

So for Dicks this exercise, we are going to be simplifying the expression the fourth root of 32 x to the fifth y to the fourth. So our first step is going to be to decompose this 32 in the product of some term and a perfect fourth power. So we&#x27;re gonna write that a 16 times two 16 is to to the fourth so we can factor that out of the radical as a two. And then why did the fourth is obviously perfect for so we can factor that outside of the radical as well, and X to the fifth can be rewritten as X of the fourth times X and X to the fourth can be brought outside the radical This goes the way this goes away. The two is inside the radical. This remaining ex term is inside the radical, and our final answer is going to be to x y Route two x

Finian Lickona · Answer

So for this exercise, we&#x27;re going to be simplifying term route eight of the fifth over, too. Now, two cannot be simplified any further, so that&#x27;s going to have to stay in the radical. But the aid of the fifth term can be rewritten as a squared times a squared times, eh? So if we bring this a squared term out and this a squared term out, we&#x27;re left with a times a out in the front of the radical, which is a squared. So our final answer is going to be a squared route. In them, we have the single A term left, and of course, the 1/2.

Problem

In $3-38$ , write each radical in simplest radica…

Problem 9 Easy Difficulty

In $3-38$ , write each radical in simplest radical form. Variables in the radicand of an even index are non-negative. Variables occurring in the denominator of a fraction are non-zero.
$$
5 \sqrt{200 x y^{2}}
$$

Answer

50$y \sqrt{2 x}$

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50$y \sqrt{2 x}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry