nment 12 Help Save&Exit Put the steps in correct order to prove that V2 is irrat

Question

nment 12 Help Save&Exit Put the steps in correct order to prove that V2 is irrational Rank the options below Suppose that 2/3 or V is the rational number p/g. where p and q are positive integers with no common factors Hence, the assumption that v2 is rational is wrong. It is erational Since o? s even q must be even Hence, p and g are both even, that is, thet 2 is a common divisor of p and q Hence, 2 1. or, equivalently, P3 2This s ottained by cubing on both sides Substituting into the equation p3-203,83 24 which simpities to 43 Thus p? is even Since the product of odd numbers is odd. pis even and hence p 2s This contradicts the choice of p/ a such thet p and q have no common factors Firetox MacBook Air 80 2

Explanation / Answer

The sequence of instructions for proof

Step 1: Line 1(suppose that 21/3 is rational number...................)

Step 2: Line 4(hence 2=p3/q3 ........................................)

Step 3: Line 6(thus p3 is even.........................)

Step 4: Line 5(substituting into eq p3=2q3.......................................)

Step 5: Line 3(since q3 is even ........................................)

Step 6: Line 7(thus contradicts the choice of p/q .......................................)

Step 7: Line 2(hence the assumption that 21/3 is wrong..................................)  

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.