1. Oct 16, 2007

### hashimcom

hi
i m hashim i want to solve a qquestion
1.if x is rational & y is irrational proof x+y is irrational???
2. if x not equal to zero...y irrational proof x\y is irrational??
3.if x,y is irrational ..dose it implise to x+y is irrational or x*y is irrational

thanks
hashim

Last edited by a moderator: Oct 16, 2007
2. Oct 16, 2007

### d_leet

1. is easy, what have you tried so far?
2. Do you mean x/y? And is x supposed to be rational? If not then 2 is false.

3. Oct 16, 2007

### sutupidmath

1. since x rational we can write it as p/q, where they cannot be simplifyed anymore.
suppose now that x+y is rational,
so it also can be written like r/s, where r,s are integers
so x+y=r/s,

p/q +y=r/s , y=r/s -p/q, so we come to a contradiction, since the right hand of the equation is also a rational, but it contradicts the fact that y is irrational, so our first assumtion that x+y is rational is wrong.

4. Oct 16, 2007

### sutupidmath

3. for the it looks like trivial.

5. Oct 16, 2007

### hashimcom

what it mean????

& where num 2 proof

hashim
thanks

6. Oct 16, 2007

### sutupidmath

well, i am not going to show u the whole proof for the last one. But try to reason the same way i did on problem 1.

7. Oct 16, 2007

### hashimcom

mr sutupidmath ....
czn u say my proof for 2
pf:
since x non zerc, so x either rational or irrational
i. if x rational & x non zero.......
x =p\q wher p,q is intger...
y is irrational.
now suppose x\y is rastional
x\y=r\s....r,s is integer.
x\y=(p\q)\y=r\s
ii. x is irratinal, x non zero....y irrational
suppose x\y = r\s
x = r\s*y.........how to continue now?????

thanks
hashim

8. Oct 17, 2007

### HallsofIvy

Staff Emeritus
The way you have stated it, "2. if x not equal to zero...y irrational proof x\y is irrational", it's NOT true! For example, $\pi/\pi= 1$. The ratio of two irrational numbers certainly can be rational. You probably meant: If x is a rational number, not equal to 0, and y is irrational, then x/y is irrational. For all of these, you don't need to go back to the definition of rational numbers as m/n. Use the fact that the rational numberse are closed under the operations of addition, subtraction, multiplication, and division (with divisor not 0).

9. Oct 17, 2007

### sutupidmath

10. Oct 17, 2007

### d_leet

11. Oct 17, 2007

### sutupidmath

ok then, what could we say as a conclusion at this case. Because obviously we cannot conclude that at any case when x and y are irrational x/y is rational. FOr example, sqr3/sqr2 is irrational, or sqr6/sqr3, is obviously irrational.

12. Oct 17, 2007

### d_leet

You can't say anything, sometimes it's rational, sometimes it isn't.