Question

In the style of the proof that square root of 2 is irrational, prove that the...

  1. In the style of the proof that square root of 2 is irrational, prove that the square root of 3 is irrational. Remember, we used a proof by contradiction. You may use the result of Part 1 as a "Lemma" in your proof.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Discrete Structures question In the style we used to show that the square root of 2...
Discrete Structures question In the style we used to show that the square root of 2 is irrational, show that the square root of six is irrational. You should use the following lemma in your proof: If n2 is a multiple of 6, then so is n (for any integer n).
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square...
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square root of 17 is irrational too, for any natural number n. use the following lemma: Let p be a prime number; if p | a2 then p | a as well. Indicate in your proof the step(s) for which you invoke this lemma. Check for yourself (but you don’t have to include it in your worked solutions) that this need not be true if...
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square...
Prove that the square root of 17 is irrational. Subsequently, prove that n times the square root of 17 is irrational too, for any natural number n. use the following lemma: Let p be a prime number; if p | a2 then p | a as well. Indicate in your proof the step(s) for which you invoke this lemma. Check for yourself (but you don’t have to include it in your worked solutions) that this need not be true if...
Prove that the (square root of 3)/3 is irrational.
Prove that the (square root of 3)/3 is irrational.
Prove that the square root of 5 is irrational.
Prove that the square root of 5 is irrational.
(1) Let x be a rational number and y be an irrational. Prove that 2(y-x) is...
(1) Let x be a rational number and y be an irrational. Prove that 2(y-x) is irrational a) Briefly explain which proof method may be most appropriate to prove this statement. For example either contradiction, contraposition or direct proof b) State how to start the proof and then complete the proof
Prove that there is no positive integer n so that 25 < n^2 < 36. Prove...
Prove that there is no positive integer n so that 25 < n^2 < 36. Prove this by directly proving the negation.Your proof must only use integers, inequalities and elementary logic. You may use that inequalities are preserved by adding a number on both sides,or by multiplying both sides by a positive number. You cannot use the square root function. Do not write a proof by contradiction.
Prove that there is no positive integer n so that 25 < n2 < 36. Prove...
Prove that there is no positive integer n so that 25 < n2 < 36. Prove this by directly proving the negation. Your proof must only use integers, inequalities and elementary logic. You may use that inequalities are preserved by adding a number on both sides, or by multiplying both sides by a positive number. You cannot use the square root function. Do not write a proof by contradiction.
Ex 2. Prove by contradiction the following claims. In each proof highlight what is the contradiction...
Ex 2. Prove by contradiction the following claims. In each proof highlight what is the contradiction (i.e. identify the proposition Q such that you have Q ∧ (∼Q)). Claim 1: The sum of a rational number and an irrational number is irrational. (Recall that x is said to be a rational number if there exist integers a and b, with b 6= 0 such that x = a b ). Claim 2: There is no smallest rational number strictly greater...
Prove the statement " For all real numbers r, if r is irrational, then r/2 is...
Prove the statement " For all real numbers r, if r is irrational, then r/2 is irrational ". You may use any method you wish. Be sure to state what method of proof you are using.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT