Archive
9th of September 2015
Mathematics
Q:

proove that Route 5 is irrational

Nikunjgoel123 Goel - CBSE - Class X

Tuesday, September 08, 2015 at 16:21:PM

A:

W e space n e e d space t o space p r o v e space t h a t space square root of 5 space i s space i r r a t i o n a l. O n space t h e space c o n t r a r y comma space l e t space u s space a s s u m e space t h a t space square root of 5 space i s space r a t i o n a l. rightwards double arrow square root of 5 equals p over q comma space q not equal to 0 rightwards double arrow q square root of 5 equals p S q u a r i n g space b o t h space t h e space s i d e s space o f space t h e space e q u a t i o n comma space w e space h a v e comma 5 q squared equals p squared T h a t space i s space 5 space d i v i d e s space p squared. rightwards double arrow p squared equals 5 k comma space w h e r e space k space i s space s o m e space c o n s tan t rightwards double arrow p equals 5 r comma space w h e r e space r space i s space s o m e space c o n s tan t rightwards double arrow p space a n d space q space a r e space h a v i n g space c o m m o n space f a c t o r space 5 comma space w h i c h space i s space a space c o n t r a d i c t i o n. rightwards double arrow H e n c e space o u r space a s s u m p t i o n space t h a t space square root of 5 space i s space r a t i o n a l space i s space i n c o r r e c t. rightwards double arrow square root of 5 space i s space i r r a t i o n a l.

Wednesday, September 09, 2015 at 18:09:PM