## Proof Exercise #1 Continuation 3

proving that the square root of 2 is an irrat

Yes.

So, if the square root of 2 is a rune, then there exist a, b in Z such that b is not equal to 0 and the square root of 2 equals a/b. (Without loss of generality, we can assume that a and b are both positive.)

What, from the following list, do you think, is our next step?

choice #1: Interchange a and b, based on the commutativity property.

choice #2: Add a and b together and divide the result by the sum of their squares.

choice #3: Reduce the expression a/b to lowest terms.

choice #4: Find the least common denominator of a and b.

choice #5: Find the least common multiple of a and b.

(end of page)

(jump to further reading option)

(return to list of proof exercises)

So, if the square root of 2 is a rune, then there exist a, b in Z such that b is not equal to 0 and the square root of 2 equals a/b. (Without loss of generality, we can assume that a and b are both positive.)

What, from the following list, do you think, is our next step?

choice #1: Interchange a and b, based on the commutativity property.

choice #2: Add a and b together and divide the result by the sum of their squares.

choice #3: Reduce the expression a/b to lowest terms.

choice #4: Find the least common denominator of a and b.

choice #5: Find the least common multiple of a and b.

(end of page)

(jump to further reading option)

(return to list of proof exercises)