Question
prove or disprove the following statement.
Irrational numbers of the form a+√b are closed under multiplication where a and b are natural numbers
Irrational numbers of the form a+√b are closed under multiplication where a and b are natural numbers
Answers
Steve
I don't think it's true
(2+√3)(5+√7) = 10+2√7+5√3+√21
I don't think that can be reduced to a+√b
Note, however, that a+b√D where D is fixed do form a quadratic field, which is closed under multiplication.
(2+√3)(5+√7) = 10+2√7+5√3+√21
I don't think that can be reduced to a+√b
Note, however, that a+b√D where D is fixed do form a quadratic field, which is closed under multiplication.