Question: Prove that if x is irrational and x 0, then x is irrational.

Prove that if x is irrational and x ≥ 0, then √x is irrational.

Step by Step Solution

★★★★★

3.47 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We give a proof by contraposition that i... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

923-M-C-M-S (1405).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

Prove that if x is irrational, then 1/x is irrational.

Q:

Prove each implication by contradiction, (a) If x and y are positive numbers, then x + y x + y. (b) If x is irrational and y is rational, then x + y is irrational. (c) If 13 people are selected, at...

Q:

Let X be a metric space. a) Prove that if E X is compact, then E is sequentially compact (see Exercise 10.1.10). b) Prove that if X is separable and satisfies the Bolzano-Weierstrass Property, then...

Q:

Need help with #1 and #8 especially Need help with #1 and #8 especially (5 points) a. Translate the following sentence into logic, using the provided predicates: "No one has been to every city in...

Q:

From Exercise 8.14) Prove: Irrational(x) Irrational(). [Hints: An irrational number is a number that cannot be expressed as a fraction with a whole number in both the numerator (the top) and the...

Q:

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2015 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

Q:

MAT 137Y: Calculus! Problem Set 9. Due in tutorial on March 21-22 Instructions: Print this cover page, ll it out entirely, and STAPLE it to the front of your problem set solutions. (You do not need...

Q:

38. Prove that if x is irrational, then x is irrational

Q:

Can someone help me explain this proof? ESSAY. Write your answer in the space provided 6) Prove that if x is irrational, then 1/x is irrational

Q:

Prove that if x is irrational, then 1/x is irrational.

Q:

A square bar of a length Im and cross sectional area 400 mm, is subjected to a tensile load of 10 KN. If the modulus of elasticity of the bar material (E) is 200 GN/m. Determine the change in the...

Q:

Wooden Toys Inc. produces two wooden toys: boat and train. A boat toy sells for 27 SAR. It costs the company 10 SAR for raw materials and 14 SAR for labor. Similarly, a train toy sells for 21 SAR and...

Q:

Which of the following best describes a bond with a call feature? None of the answers provided are correct The leverer munt ary shigher coupon if the bond is called. The bondholder has the right to...

Q:

Consider the National Football League data in Table B.1. a. Fit a multiple linear regression model relating the number of games won to the team s passing yardage ( x2 ), the percentage of rushing...

Q:

Suppose that X is a Poisson random variable, where pX(k) = ek/k!, k = 0, 1, . . . . (a) Does the random variable W = 3X have a Poisson distribution? (b) Does the random variable W =3X +1 have a...

Q:

Suppose that Y is a normal variable, where (a) Does the random variable W = 3Y have a normal distribution? (b) Does the random variable W = 3Y + 1 have a normal distribution? (1/-/2 ) exp

Q:

Find the expected value of e3X if X is a binominal random variable with n =10 and p = 1/3.

Q:

SanData Inc. recently paid its annual dividend of $ 3 . 6 2 . Dividends have consistently grown at a rate of 5 % . You estimate that the stock has a required return of 1 5 % . What is the intrinsic...

Q:

iN '06 ABC Company is considering the purchase of an asset which would cost $100,000. The '06 information includes the impact of this asset. All changes from '05 to '06 can be attributed to the...

Q:

You are currently re-evaluating your payables policy. Your current suppliers offer terms of 1.5/10, net 40 with a late payment fee of 1.5% per month. A supplier wanting your business is willing to...