Explain why the sum, the difference, and the product of two rational numbers are again rational numbers. Is the product of two irrational numbers again irrational? What about the sum?

Question

anonymous · Answer

please somebody help me :(

perl · Answer

hello

perl · Answer

the sum of two rational numbers is rational , proof:
given p/q, r/s , q and s are both non zero  (because division by zero is undefined). 
now is p/q + r/s = a rational # ?

perl · Answer

yes it is , because p/q + r/s = ( ps + rq) / (q*s), and we assumed both q and s are non-zero. and ps+rq is an integer, qs is an integer. so this is a ratio of two integers, so this is rational

perl · Answer

the sum and product of two irrational numbers is not necessarily irrational 
(3+sqrt(2) + (3-sqrt(2)) = 6 
sqrt(2) * sqrt(2) = 2

anonymous · Answer

how about the difference and the product?

anonymous · Answer

thanks alot :)

perl · Answer

sure thing

anonymous · Answer

ummm..sorry..can you explain why?

anonymous · Answer

hello?

anonymous · Answer

product of two irrational numbers is a rational number some times
like

anonymous · Answer

|dw:1359973552447:dw|