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

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.
$$
\sqrt{32}
$$

Nick Johnson · Accepted 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

So here we have the square root off 12. Okay. What? This could be rewritten as just a square root. 12 is well four times three. Right. So the square root of 12 is just a square root of four times three. But then once you have a product ins under your square root, you can and separate this. This is equal to the square root of four times the square root of three. Or you can think of it like once you have a perfect square. The squid of four is too. So that would come outside of your radical and that you&#x27;re still left with a three underneath your radical. So the square root of four times three that&#x27;s equal to to write the square four is, too. But then times the square root of three. So therefore the square root of 12 is equal to two times the square root of three. All right, take her

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,

Finian Lickona · Answer

So for this exercise, we are going to be simplifying the term. The cube root of a cubed over three Now three is not a perfect cube, so it&#x27;s gonna have to stay inside the radical. But a cubed is obviously a perfect cube, so we can factor that outside of the radical. Just put it right here. So our final answer is actually going to just be a times the cube root of one over three.

Finian Lickona · Answer

So for this exercise, we want to simplify the term cube root of 16. So if we want to rewrite 16 as a product of a perfect cube in some other term, we can write it as eight times to now. The cube root of eight is, of course to, so we can bring that out as a two coefficient and then we have to leave this remaining two under the radical, so our final answer is 22

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

Problem

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

Problem 5 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.
$$
\sqrt{32}
$$

Answer

4$\sqrt{2}$

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

4$\sqrt{2}$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry