in-3-38-write-each-radical-in-simplest-radical-form-variables-in-the-radicand-of-an-even-index-ar-16

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.
$$
\sqrt{\frac{4 a^{4}}{25}}
$$

Nick Johnson · Accepted Answer

we have the square root of 48 to the fourth all over 25. So well, I see as a lot of perfect squares under this square root. So this is equal to actually write this as the square root of well off 48 to the fourth over the square root of 25 then notice how in the numerator four is a perfect square and so is a to the fourth right with the numerator can be rewritten that we written as the square root of four times the square root of aid to the fourth over. The square root of 25 a square before is just equal toe to right in the square root of aid to the fourth. That&#x27;s a square, because a square times a square is a to the fourth, so we have to just to a square in our numerator. And then, of course, the square root of 25 is just equal to five. So this is going to simplify down to well to a squared over 25

Finian Lickona · Answer

So for this exercise, we are going to be simplifying the term the cube root of 48 to the fourth power. So if we decompose the 40 into perfect Cuban, some other term we get eight times 58 is a perfect cube and then the aid of the fourth can be rewritten is eight of the third time&#x27;s A so we can bring this eight out and the state of the third term out. So our final answer is going to be two A third route que group, whatever you wanna call it five.

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.

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

so you&#x27;re given the square root of 32. So the square to 32 well, that could just be rewritten, right as the square root of well, 16 times to write 16 times two is 32 and then once you have a product underneath your square root, you go ahead and in separate. This, the square root of 16 times two is equal to the square root of 16 times. The square root of two or two square with a 16 is just four right. What? You have a perfect square under your square root. You can just pull that the perfect square out and you&#x27;re still left with. Then here, a two under your radical on the square root. So the square root of 16 times two is equal to the square 16 times square root of two, which is equal to just four times the square root of two. Therefore, um, the radical hair square root of 32 that is equal to four times the square root of two

Nick Johnson · Answer

if we have the cube root off 24 now, just like we can go ahead and begin. Break up. Right. Perfect squares. If we have a under a square root and then take out the perfect square off, we have a cube root. We can then look at perfect cubes and 24 while is a perfect cube. Um, namely eight times three rights. I can rewrite the cube root of 24 as the cube root of eight times three, which is 24. But in the cube root of eight is equal to this is equal to, um, the cube root of eight times the cube root of three. But the Cuban of it is to this is equal to two times the cube root of three. All right, you can go ahead. You can pull out your perfect cube of eight, which is too. So you pull out the two and you still left with a three under your radical under the cube root. So you have the to which you pull out with cube, which is which is right, the cube root of eight. And then we still have the three of the radical. So we have two times Big Cube, root of three. All right,

Problem

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

Problem 18 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.
$$
\sqrt{\frac{4 a^{4}}{25}}
$$

Answer

$\frac{2 a^{2}}{25}$

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$\frac{2 a^{2}}{25}$

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