in-3-38-write-each-radical-in-simplest-radical-form-variables-in-the-radicand-of-an-even-index-ar-27

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.
$$
\sqrt{\frac{9}{50 x y^{7}}}
$$

Finian Lickona · Accepted Answer

So for this exercise, we want to simplify the expression square root of nine over 50 x y to the seventh. So nine is already a perfect square, so we can factor that out as a three 50 can be decomposed into two and 25. So this 25 can be factored out as a five. That, too, is going to stay in the radical. And then this wide of the seventh can be rewritten as y squared times. Why squared times Why squared times why? So all of these y scores can come out in front of the radicals? That&#x27;s gonna be why did the third and ah, what&#x27;s left in the radical is going to be a one over to Why? So our final answer is 3/5. Why did the third squared of one over to Oh, and there&#x27;s still that ex term, of course. One over two ex wife

Finian Lickona · Answer

So for this exercise, we want to simplify the term for four radical 363 x to the fifth. Why did the seventh? So we need to look for ways to break this 363 down into a product of some term and a perfect square so we can rewrite that as three times 121 121 is 11 squared. So if we, ah, bring out all of our perfect square terms, we have three times 121 times X squared times x squared times x times y squared times y squared times y squared times Why, so we bring this out of the radical This set of the radical this out of the radical and all these out of the radical. So we have four times 11 times x times x times. Why times Why times Why and what&#x27;s left under the radical is three Thesing galex term in a single weiter. So our final answer is 44 x squared. Why cubed radical three ex wife

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

Nick Johnson · Answer

we have the square root of three acts over four Y Okay, well, that&#x27;s gonna be equal to Well, we can write that as a square root of three acts over the square root of for Why? Then notice that while four is a perfect square, you can go ahead. Can read this as one square root up three acts over what its crew before Why is so square root of four? Why, that&#x27;s equal to again. The square root of four times the square root of why prescribed for his two. That&#x27;s two times the square root of why. Okay, so in the nominee, we have two times the square root of why, um and that&#x27;s about all we can do him if you want. I mean, really, we have a 1/2 so I mean, I would say this would be on acceptable answer. We could go ahead and pull out a 1/2. So we have we have 1/2 um, well, 1/2 times Thea square root of three acts over the square root of why that would be another possible answer. Right? The same thing and there&#x27;s no more perfect squares uses. There&#x27;s really nothing else you could go on and do further. So there you have it

Nick Johnson · Answer

have the square root of three X over four wine. Well, this kid to be, um, split up as well The square root of three X over the square root of four. Why? Okay. And they can realize that end the denominator well, the square root of four times why that&#x27;s equal to the square root of four times a spirit of why right? And the square therefore is to So you have a product under your square root. If one of the things, um one of the factors in your product is a perfect square, we can pull that perfect square out to square. The four is too so squared off for why is equal to two times the square root of why so this is equal to or are. Numerator is just a square root of three acts over two times the square root of why all right,

Problem

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

Problem 29 Medium 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.
$$
\sqrt{\frac{9}{50 x y^{7}}}
$$

Answer

$\frac{2 \sqrt{10 x y}}{5 y^{2}}$

Related Courses

Algebra 2 and Trigonometry

Related Topics

Discussion

Top Educators

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

Ann Xavier Gantert

Algebra 2 and Trigonometry

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\frac{2 \sqrt{10 x y}}{5 y^{2}}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry