Show that the product of  2 irrational numbers need not be irrational giving examples.

Asked by seeni2005 | 19th Jun, 2016, 09:24: AM

Expert Answer:

begin mathsize 12px style Consider space the space following space examples.
1. space square root of 5 space and space square root of 10 space are space two space irrational space numbers
square root of 5 space cross times space square root of 10 space equals space square root of 50 space which space is space irrational
2. space space square root of 2 space and space square root of 8
square root of 2 space cross times space square root of 8 space equals space square root of 16 equals 4 space which space is space rational
3. space space square root of 12 space and space square root of 3
square root of 12 space cross times space square root of 3 space equals space square root of 36 equals 6 space which space is space rational
Thus comma space the space product space of space two space irrational space numbers space can space be space irrational space or space rational. end style

Answered by Rebecca Fernandes | 19th Jun, 2016, 12:13: PM