in-3-10-tell-whether-each-represents-a-number-that-is-rational-irrational-or-neither-sqrt3-8

Question

In $3-10,$ tell whether each represents a number that is rational, irrational, or neither.
$$
\sqrt[3]{-8}
$$

Dilip Paruchuri · Accepted Answer

All right, you guys. So in this problem, we&#x27;re given the cube root of negative eight and were asked to determine if this value is a rational number, an irrational number or neither. And so for us, let&#x27;s try to find a factory ization kind of or simplifies cube root of negative eight. So let&#x27;s start out. So we know that the cube root of negative age can also be written as the cube root of negative for times two. Or let&#x27;s write a better. It could be written as a product of four times negative, too. And we just got this cause we know that four times they give to his negative eight just a simple algebraic step. We also know that four is equal to negative two times negative, too, so we can rewrite that last step as the product of negative to have donated to the negative, too. And the next step is we can rewrite this product of three negative twos as negative too cubed. And when you take the cube root of Thumping Cube, you&#x27;re just going to get that something. And so the cube root of negative to cubed is just negative, too, so your route of negative eight. Simplified is going to equal negative. Too. Negative too, by definition is a rational number. So cube root negative eight is a rational value. Thank you for listening, guys. And I hope this helps. This was a pretty simple, straightforward problem. Then I hope I clear any doubts you guys head on.

Dilip Paruchuri · Answer

all right. Hey, guys. So in this problem, we are giving the square root of feet and we&#x27;re being asked if the square root of eight is a rational, irrational or neither we that we can determine. So let&#x27;s take a look at the squirt of eight. Now, the square root of eight weekend basically rewrite as the square root of four times two square root of four times to just algebraic steps is a square to four times the square root of two we know for is a perfect squared. Two squared is equal to four, and basically what that means is square root of four can be simplified to just two. So in a sense, squared of eight is equal to two times square root of two. And now, if we take a look at this simplification, squirt of eight is equal to two times word of two. And in that case we know that two is a rational, rational number, and we also know that square root, too, is an irrational number. So Squared eight is what I would like to say is a rational multiplied by an irrational, and this is a fact that&#x27;s gonna be very important in this chat in this section and that section, and that fact is that whenever you&#x27;re multiplying a rational, by and irrational, you&#x27;re always going to get an irrational value. So in that case, we can death definitively say that since Square eight is the product of an irrational of and ration of eight. Sorry, since Square eight is the product of a rational and an irrational, we can definitively say that&#x27;s where the eight is an irrational value. So thanks for listening, guys. And I hope this helped. And please do remember the key factor that irrational times an irrational always gives us an irrational.

James Kiss · Answer

were asked to determine if the spirit of negative eight is rational or irrational. Well, since the squared of negative eight is imaginary graze the imaginary Route of eight, which could be broken down to two times imaginary root of two. That&#x27;s a little bit irrelevant in this question because we&#x27;re asked, determine if a spirit of negative eight is rational or irrational, Rational and irrational numbers fall under the rial number system and this is imaginary, so it is neither a little bit tricky.

James Kiss · Answer

there has to determine if the scared of zero is rational or irrational or neither, and since the skirt of zero is equal to zero and zero could be written as a fraction with any of them, I&#x27;m a besides zero. Since it&#x27;s written as a fraction, it is rational.

James Kiss · Answer

because the square root of 25 is equal to the square root of five. Squared five squared is 25 and it&#x27;s heard of five. Squared is equal to five because the square root and squares are in verses of each other and by could be written as 5/1. So by the definition of a rational number, since it can be written as a fraction, that means the skirt 25 is rational.

Dilip Paruchuri · Answer

all right. Hey, guys. So this problem, we have the fourth route off 16. So basically, what we&#x27;re trying to do is determine if this value if this thing simplifies to irrational, irrational or neither value and first step, is that we&#x27;re going to try to simplify our four through eight of 16. We know 16 is the product of four times for, so let&#x27;s write that as that. So so cube so forth. Fruit of 16 is equal to four through of four times four. We also know that four can be written as two times two, so let&#x27;s rewrite each four as the product of two times, too. You have two times two times two times two. So you&#x27;re multiplying two together by itself for times. And another way to write that is as an exponents. So it&#x27;s Equus. Over two times, two times two times two is equal to two to the fourth, 40 minutes 16 is equal to four. Threw it off to to the fourth. And when you have the fourth root of something to the fourth, it&#x27;s just equal to that something. So this is just equal to two, and so we have four through of 16 is equal to two. We know two is a rational number so forth. Fruit of 16 is also a rational value.

Problem

In $3-10,$ tell whether each represents a number …

Problem 6 Easy Difficulty

In $3-10,$ tell whether each represents a number that is rational, irrational, or neither.
$$
\sqrt[3]{-8}
$$

Answer

rational

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