Question 206081
I'll do the first two to get you started.


An example of the sum of two irrational numbers may be and irrational number? The numbers {{{sqrt(2)}}} and {{{sqrt(8)}}} are both irrational and {{{sqrt(2)+sqrt(8)=sqrt(2)+2*sqrt(2)=3*sqrt(2)}}} which is also irrational.



An example the sum of two rational numbers may be a rational number? {{{1/2}}} and {{{2/3}}} are both rational. Adding them together gets us {{{1/2+2/3=3/6+4/6=7/6}}} which is also rational.