in-11-38-evaluate-each-expression-in-the-set-of-real-numbers-sqrt5-1

Question

In $11-38,$ evaluate each expression in the set of real numbers.
$$
\sqrt[5]{-1}
$$

Dilip Paruchuri · Accepted Answer

Okay, guys. So in this problem, we&#x27;re given the fifth root of negative one, and we&#x27;re being asked to simplify this expression and in the problem of states that are expression or simplified answer is gonna be in is gonna be a real number. And so let&#x27;s start off. So as we&#x27;ve been tackling most of these problems, the first step to do is to rewrite our negative one in a way that our fifth root cancels out with, uh, with the negative ones with the river in form of our negative one. By that, let me explain that the way to get rid of Fifth Root how do you get rid of him through you take the fifth root of something to the fifth power. And in that way we can get rid of the fifth through, and we&#x27;re just left with that something in the middle. And in order to do the same thing with this problem, we need to rewrite our negative one as naked as something as basically as something So the fifth power. And in order to do that, we&#x27;re just gonna factor it out. We&#x27;re gonna see what mould, what? Five things multiplied by itself gives us negative one and thinking about that we get that negative one is actually just native one times itself five times. Now, why is that true? If you just think about it, we know that negative one times negative one is one. No, no, One times negative one is negative. One negative, one times negative One is one and one times negative. One is native simple calculations. And basically, from this, we could basically rewrite fifth root of negative one as the fifth root of negative one to the fifth power and going back to this step right here, the way we cancel out the fifth root is if we have taken the fifth period of something to the fifth Power. We just get that something. This case, we&#x27;re taking the fifth root of negative one to the fifth power, and as a result, we just getting negative one. So because of these steps, we can literally see that fifth root of negative one is just equal to negative one. Negative one is in the reels. So this satisfies the conditioner problem gave that our expression answer should be in the reels. And just to recap the key step that we made right here is that we connected. Negative one is where we basically made the, uh, algebraic step That negative one is equal to negative one to the fifth power. And that&#x27;s basically what allowed us to cancel out the fifth root and come down to our final expression. That fifth root of negative one is just equal to you. Negative one. Thank you for listening, guys. And I

Dilip Paruchuri · Answer

All right. Hey, guys. So, in this problem, we&#x27;re taking the fifth root of negative one over 32. The problem asks us to simplify this expression, and it states that are answers should be something in the real play, the real numbers. And so let&#x27;s tackle this problem with them Algebraic steps, basically rewriting what we&#x27;re given first. So we&#x27;re given the fifth root of negative one over 32. Now, what we can do is we can do this next step where we basically split the fifth root apart into the numerator and into the denominator. So we have We&#x27;re taking the fifth root of the numerator, and then we&#x27;re taking the fifth root of the denominator. Now let&#x27;s take a look at the numerator first, the numerator. Well, in a previous problem, well, we already did a problem like this. We said our fifth root of negative one is basically the same as fifth root of negative one to the fifth. Because in that problem, we saw the negative ones of the fifth is equal to negative one. And when you take the fifth would have something to the fifth u get net. You get that something So when you take 1/5 root of negative one to the fifth u get negative want. So from this, we can easily see that our numerator evaluates to negative one. And now we take a look at her denominator. So, like that previous problem, we want to do a similar thing we want to find. We want to cancel our fifth root out, and the way we do that is, if we take the fifth root of something to the fifth. So we want to rewrite our 32 as some number two, the fifth Power. And luckily through algebra, um, we see that 32 is actually equal to two to the fifth. So you multiply two times itself five times and you get 32. And so when you do that, fifth root of two to the fifth is going to be equal 22 and two to the fifties 32. So we know that fifth root of 32 is just equal to two. So our answer is negative. 1/2 show negative. 1/2 is the answer to the radical expression. Ah, fifth root of negative of negative one over 32. Now just to, uh I&#x27;m just gonna say this verbally because there is another way we could have tackle this problem. We could have tackle this problem through a In this problem, we tackle the problem by splitting up, splitting our radical into the numerator and denominator. But what? But what we could have also done is we could have done the fifth root of negative one times the fifth root of one over 32. And in doing this, we could have just solved each of these individually and you get negative one times one have. And then you would still hopes you would still get your answer to be, uh, negative 1/2. Just if you used this way to solve the problem. What happened is you just need to recognize that one over 32 is just equal to 1/2 to the fifth power. Just say if you get the same ends or just a different process, different approach. Thanks for listening, guys. And I hope this

James Kiss · Answer

were asked to find the Q route of zero 0.0 01 Well, thank you, Root no clean 001 is the same thing as the Cube root. A 0.1 to third 0.1 of the third is 0.1 Now that we run, it is the perfect Q Bar Cube root and are perfect. You counter act there in verses of each other, and now this tells us that the cube root of 0.1 is simply zero 0.1.

James Kiss · Answer

were asked to evaluate the square root of 16. The square root of 16 is the same as that the square root of four squared because four squared is equal to 16 square roots and squares are in versions of each other, so they counter act. So when looking at this as the square root of four squared, it&#x27;s the same thing is four for is our answer.

James Kiss · Answer

we were asked to evaluate the negative square root from 16. The negative spirit of 16 is the same as the negatives. Gray route of four squared because four squared is the same as 16. And now, since square roots and squares are inverse, is the square root in this fair? Cancel each other out, so we&#x27;re just left with negative or and that is arranged.

Dilip Paruchuri · Answer

Hey, guys, showing this problem. We&#x27;re given the fourth root of 16 and with 1/4 rate of 16 we&#x27;re being asked to, um, simplify the fourth rate of 16 and 432 16 if I simplify that out is the same thing as four time. It&#x27;s with Gillian as four times for And if I simplify and factor that even further, that&#x27;s the same thing as the fourth root of two times. Two times, two times two Basically two times itself four times, two times itself four times is just another way of saying to to the fourth. And so the four through eight of 16 is equal to the fourth root of to the fourth. So whenever you take the four the root of something to the fourth, you&#x27;re going to get that something back. And that&#x27;s something in this case is too. Oh, by the way, this step right here the better. I&#x27;m gonna rewrite that better right here. This is how the step should actually look like, so it should look like four through two of two in parentheses in the four outside of it. Just a small mistake on my part here, But everything else the fourth root of 16 were saying is equal to two. So that&#x27;s gonna be our answer to this simple fire expression. Off four through eight of 16.

Problem

In $11-38,$ evaluate each expression in the set o…

Problem 24 Hard Difficulty

In $11-38,$ evaluate each expression in the set of real numbers.
$$
\sqrt[5]{-1}
$$

Answer

$-1$

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