5

If a is a nonzero rational number and b is irrational, then a/b is irrational....

Question

If a is a nonzero rational number and b is irrational, then a/b is irrational.

If a is a nonzero rational number and b is irrational, then a/b is irrational.



Answers

(a) If $a$ is rational and $b$ is irrational, is $a+b$ necessarily irrational? What if $a$ and $b$ are both irrational? (b) If $a$ is rational and $b$ is irrational, is $a b$, necessarily irrational? (Careful!) (c) Is there a number $a$ such that $a^{2}$ is irrational, but $a^{4}$ is rational? (ch) Are there two irrational numbers whose sum and product are both rational?

We used to determine of the statements are true. So first of all have to ration numbers are added up, but all was not irrational number. So this is for six A. So we know that after a rash number and they're out of that was always going to become a rational number. No, this is because now a lot of what two fractions added up together can always become a fractions who know that this is true for six be were us. If if to irrational numbers add up our roles and irrational number was simple way to prove this wrong. It's just too given examples. We up I minus part, it's equal to zero, which is a rational number. And so because of this, we know that this is not true.

But we want to prove or disprove that if a and B a rational numbers, then A to B is also so this is just walk through at all. So to prove we just need Thio want to describe this? We just need to come up with a counter example. So there's a counter example Everyone knows that square off to is not rational. So what we'll do is we'll just set up the example where a easy to which is still a raffle number. And he also said, B to be won over to which is some rational number as well. Then A to the B is equal to 2 to 1 over two, which is square off to which is not rational, hence the statement is false.

You know that by is way can do some. Uh I am be heaven to buy here. Yes, I would have by Plus I would too. Times I don't want one word, you fi and then left for visiting brass that I square blessed be square with a Jew My square blessed by Jews My square by square, Our farm We called you. My advice far is

Hello. So here I want to find um if the product of irrational and irrational is necessarily rational or irrational. So here let's go ahead, let's let a B B equal to see where A. Is rational and B. Is irrational. Now let's suppose that C. Is rational. Then the only possibility is that A. Is equal to see which is equal to zero. Um Because if the above conclusion is not true, in other words if A is not equal to zero then so if A is not equal to zero then um B. Which would be then be equal to see over A. And C and A. Are both rational, which then would imply that B is also rational, but this is the contradiction. So because we have again that B is irrational. So here we have a contradiction. Um So that would then imply that C must be irrational. She must be Irrational Whenever A. is not equal to zero.


Similar Solved Questions

5 answers
9. Let f : A - B, where A and B are nonempty sets: Prove that if Ti, Tz € B, then f-1(T UT2) = f-1(Ti) U f-1(T2)
9. Let f : A - B, where A and B are nonempty sets: Prove that if Ti, Tz € B, then f-1(T UT2) = f-1(Ti) U f-1(T2)...
5 answers
2) Consiter ghe curte KIVGT brv tha Danequalion6t2 -6 & 126 &McvrtticulFndpolnthe
2) Consiter ghe curte KIVGT brv tha Dan equalion 6t2 -6 & 12 6 & Mc vrtticul Fnd polnth e...
5 answers
Lemii.49-3 7Chris Koszeghy; AttemptQuestion 20 points)Calcume hefolla ing] strong basy and srong acid solutions 0.075 M Caiohiz 0,048 HNO]FcaatQuestion 21 (2.5 points)Consider tho lollawwing in reversible reacion:
Lemii.49-3 7 Chris Koszeghy; Attempt Question 20 points) Calcume he folla ing] strong basy and srong acid solutions 0.075 M Caiohiz 0,048 HNO] Fcaat Question 21 (2.5 points) Consider tho lollawwing in reversible reacion:...
5 answers
FindNeed Help equatlon the 1 consistingpolnts thatequidistant 1 the Land
Find Need Help equatlon the 1 consisting polnts that equidistant 1 the L and...
5 answers
Ofanp ?6the following: Let be an integer, then n is even if and only if 5n + 4 is even_
Ofan p ?6 the following: Let be an integer, then n is even if and only if 5n + 4 is even_...
5 answers
Consider the following axioms:Al: Each point is incident with exactly two lines AZ: For any two distinct lines there exactly one point incident with both lines A3: There are exactly four lines
Consider the following axioms: Al: Each point is incident with exactly two lines AZ: For any two distinct lines there exactly one point incident with both lines A3: There are exactly four lines...
5 answers
Fundoracutdls Sectidmldiqegtntal Equatdnu 9h_EaiilnIniqaticy 9aut0Zlbelyiyy thudush *t(xy)Jatehulic bin sides 64)257 NxHOw din thc_katside Stuy the Slur
Fundoracutdls Sectidml diqegtntal Equatdnu 9h_Eaiiln Iniqaticy 9aut0 Zlbelyiyy thudush *t (xy) Jatehulic bin sides 64)257 Nx HOw din thc_katside Stuy the Slur...
5 answers
#o1 atuve in O The te mper Luas re Cordled certain iOn Iotiqwo fox months: each ny ^ tcmperatuve UaS The 78F with 0 Stanard (03. 72p, What can 'efad d eviati 6 5 about +nQ dat determine with Chs by She v'$ 47igj Fnequali with K 3 % 0l had 0+ leas + days between anderatvJ { F
#o1 atuve in O The te mper Luas re Cordled certain iOn Iotiqwo fox months: each ny ^ tcmperatuve UaS The 78F with 0 Stanard (03. 72p, What can 'efad d eviati 6 5 about +nQ dat determine with Chs by She v'$ 47igj Fnequali with K 3 % 0l had 0+ leas + days between anderatvJ { F...
5 answers
20 1816 14 12 FREQUENCY 10222320 AGE186116Examine this histogram. What is the minimum value in this data?019
20 18 16 14 12 FREQUENCY 10 22 23 20 AGE 18 61 16 Examine this histogram. What is the minimum value in this data? 019...
5 answers
For the following reaction that transforms a nitrile into an amide, explain how will use IR spectroscopy to monitor the progress of the reaction. you HCI R-_C==N 40 %C "NHz Nitrile Amide (What signals would disappear and/or appear to let you know the reaction has been successful)
For the following reaction that transforms a nitrile into an amide, explain how will use IR spectroscopy to monitor the progress of the reaction. you HCI R-_C==N 40 %C "NHz Nitrile Amide (What signals would disappear and/or appear to let you know the reaction has been successful)...
5 answers
Is 8 = EYi/ Eri an unbiased estimator of 8? Show work_ Find the variances of B and B. If you already found the variance of B from Problem 3 then you don 't need to find it again. Which estimator has smaller variance? Which estimator is better estimator? And why? Show work:
Is 8 = EYi/ Eri an unbiased estimator of 8? Show work_ Find the variances of B and B. If you already found the variance of B from Problem 3 then you don 't need to find it again. Which estimator has smaller variance? Which estimator is better estimator? And why? Show work:...
5 answers
(Exercise 3.1.15 Lecture H) Cousider the first order systelu of dilfercutial equationsAludJtv-Find the coordinatus o the equillbritm point for tbis sxetenu 18 tlie point (ron W)for wlich # = ana
(Exercise 3.1.15 Lecture H) Cousider the first order systelu of dilfercutial equations Alud Jtv- Find the coordinatus o the equillbritm point for tbis sxetenu 18 tlie point (ron W)for wlich # = ana...
5 answers
Consider an electron in a 3p sublevel:What are the possible values of ℓ? (2 points)What are the possible values of mℓ? (3 points)What are the possible values of L2 and Lz? (4points)What is the value of θ when ℓ = 1 and m = 1? (2 points)
Consider an electron in a 3p sublevel: What are the possible values of ℓ? (2 points) What are the possible values of mℓ? (3 points) What are the possible values of L2 and Lz? (4 points) What is the value of θ when ℓ = 1 and m = 1? (2 points)...
5 answers
(d) d((t + Wt)n )
(d) d((t + Wt)n )...
5 answers
The forearm in the figure is held at 50.0" t0 the upper arm; and a 15.0 kg mass is held in the hand, What is the magnitude of the force exerted on the forearm by the biceps - muscle? (Neglect the weight of the forearm and take that the bicep force is direction) acting in the vertical 6) Find the magnitude of the force exerted by the elbow on the forearm;A?5-Oo(m
The forearm in the figure is held at 50.0" t0 the upper arm; and a 15.0 kg mass is held in the hand, What is the magnitude of the force exerted on the forearm by the biceps - muscle? (Neglect the weight of the forearm and take that the bicep force is direction) acting in the vertical 6) Find t...

-- 0.021793--