in-3-38-write-each-radical-in-simplest-radical-form-variables-in-the-radicand-of-an-even-index-ar-24

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.
$$
\sqrt{\frac{5 a}{18}}
$$

Nick Johnson · Accepted Answer

the square root of five a over 18 so this can be rewritten as this is equal to the square root of five egg while over the square root of 18. But 18 is well nine times to right, and nine is a perfect square. So the squared nine times two is to squirt at nine times the square to to, and it&#x27;s got a nine history. So this is equal to the square root of five a. Over Well, the square root of nine is reason that this squid of 18 is equal to three times the square root of two. So we have the square root of five a over three times the square to to all right thinking.

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.

Nick Johnson · Answer

the square root of 0.5. Well, this is equal to the square of 2.5. That&#x27;s a square root of 1/2. Right. And it&#x27;s good of 1/2 that&#x27;s equal to the square root of one over the square root of two. What city was the one right over the square root of to you? Well, then you can go ahead. And I guess I mean simplifying, I guess. Means could do here is rationalized that nominator. Um, not actually simpler or not again, I would again and there was anything wrong leaving your answer as well. This burger 2.5. Go ahead and evaluate this. Um, but again, you can realize this equal to, well, one over score, too. So you can go ahead and buy one in the form of square to over the square to to give you while one times go to two is square to to and scored a two times per two is just too. So we get square to over to is equivalent to saying square root of one house

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

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

Finian Lickona · Answer

All right, so we want to write the quantity square root of 50 as its simplest radical. For So, To do this, we&#x27;re going to look for ways in which we can decompose the value 50 into a product of some number and a perfect square. So if we ah, think of our perfect squares, they are one for 9 16 25 36. And we notice that 50 is the product of two and 25. So we can rewrite it as two times 25. And if we split those radicals apart, we get this squared of two times. The square root of 25 in the square root of 25 is, of course, five. So our final answer is square to two is just squared of two. So it can&#x27;t be simplified any further, but we have that five simplified terms. So our final answer is just five to

Problem

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

Problem 26 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.
$$
\sqrt{\frac{5 a}{18}}
$$

Answer

$\frac{\sqrt{5a}}{3 \sqrt{2}}$

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$\frac{\sqrt{5a}}{3 \sqrt{2}}$

Algebra 2 and Trigonometry

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Algebra 2 and Trigonometry