This one seems easy...but I don't think I'm coming up with something solid enough for an official, well-explained proof:
Provide a Counterexample: Every rational number is equal to the product of two irrational numbers
How would you guys go about this seemingly easy counterexample-proof? You obviously can't just say 2*1 = 2 claiming 2 is the product of two rational #'s, right?
2007-12-02 18:28:26 · 3 answers · asked by netsurfer733 2 in Science & Mathematics ➔ Mathematics
How about 0 = a * b
Can you find a pair of irrational values a & b that would make that true?
Let's solve for a:
a = 0/b
a = 0
Oops, that's not irrational...
So you can't write every rational number as a product of two irrational numbers.
2007-12-02 18:38:51 · answer #1 · answered by Puzzling 7 · 3⤊ 0⤋
There are no counterexamples, the statement is true. Two, for example is equal to the product of sqrt(2) x sqrt(2), and you can construct similar examples for any number you please.
2007-12-03 02:41:25 · answer #2 · answered by Anonymous · 0⤊ 1⤋
â6 = â3 * â2
So its not true as â6 is not a rational number.
2007-12-03 02:32:41 · answer #3 · answered by Ian 6 · 0⤊ 3⤋