prove that 2square root of 7+5 is irrational.

Asked by sudhindra2001 | 3rd Jun, 2015, 06:10: PM

Expert Answer:

We shall prove this by method of contradiction.
Let us start by assuming that 
2 square root of 7 plus 5 space i s space a space r a t i o n a l space n u m b e r. H e n c e comma space w e space c a n space w r i t e space 2 square root of 7 plus 5 equals p over q comma space w h e r e space p space a n d space q space a r e space i n t e g e r s space a n d space q not equal to 0. H e n c e comma space 2 square root of 7 equals p over q minus 5 comma space w h i c h space i s space a l s o space r a t i o n a l H e n c e comma space square root of 7 equals 1 half open parentheses p over q minus 5 close parentheses comma space a space r a t i o n a l space n u m b e r. B u t space t h i s space i s space a space c o n t r a d i c t i o n comma space a s space w e space k n o w space t h a t space square root of 7 space i s space a n space i r r a t i o n a l space n u m b e r. H e n c e comma space o u r space i n i t i a l space a s s u m p t i o n space t h a t space 2 square root of 7 plus 5 space i s space a space r a t i o n a l space n u m b e r space i s space n o t space t r u e. space H e n c e comma space 2 square root of 7 plus 5 space i s space a n space i r r a t i o n a l space n u m b e r.

Answered by satyajit samal | 4th Jun, 2015, 03:32: PM