## Proof Exercise #1 Continuation 1

proving that the square root of 2 is an irrat

Yes.

We will first show that if 2 divides the square of an integer, it also divides the integer.

What, do you think, will be our technique, from the following list, to prove that if 2 divides the square of an

integer, it also divides the integer?

choice #1: Use one of the cases of Pythagorean triples.

choice #2: Use the fact that the square of an odd number is odd.

choice #3: Investigate the cardinality of the set of even primes.

choice #4: Solve the quadratic equation whose leading coefficient is unity, whose middle coefficient is 2,

and whose constant term is 3.

choice #5: Find a geometric progression that sums to 1/2.

(end of page)

(jump to the further reading option)

(return to list of proof exercises)

We will first show that if 2 divides the square of an integer, it also divides the integer.

What, do you think, will be our technique, from the following list, to prove that if 2 divides the square of an

integer, it also divides the integer?

choice #1: Use one of the cases of Pythagorean triples.

choice #2: Use the fact that the square of an odd number is odd.

choice #3: Investigate the cardinality of the set of even primes.

choice #4: Solve the quadratic equation whose leading coefficient is unity, whose middle coefficient is 2,

and whose constant term is 3.

choice #5: Find a geometric progression that sums to 1/2.

(end of page)

(jump to the further reading option)

(return to list of proof exercises)