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Home / Doubts and Solutions/CBSE/Class 5/Mathematics

show that 2-square root of blank end root3  is   an  irrational no

Asked by nisha_vini29 6th April 2015, 9:12 PM
Answered by Expert
Answer:

W e space n e e d space t o space s h o w space t h a t space 2 minus square root of 3 space i s space i r r a t i o n a l space n u m b e r. L e t space u s space p r o v e space t h i s space b y space t h e space m e t h o d space o f space c o n t r a d i c t i o n. A s s u m e space t h a t space 2 minus square root of 3 space i s space r a t i o n a l space n u m b e r. rightwards double arrow 2 minus square root of 3 equals p over q comma space q not equal to 0 rightwards double arrow square root of 3 equals 2 minus p over q p over q space i s space a space r a t i o n a l space n u m b e r space a n d space 2 space i s space a space r a t i o n a l space n u m b e r. 2 minus p over q space i s space t h e space d i f f e r e n c e space o f space r a t i o n a l space n u m b e r s comma space 2 space a n d space space p over q comma space a n d space h e n c e space 2 minus p over q space i s space a space r a t i o n a l space n u m b e r. rightwards double arrow square root of 3 space i s space a space r a t i o n a l space n u m b e r B u t square root of 3 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 space o u r space a s s u m p t i o n space t h a t space 2 minus square root of 3 space i s space r a t i o n a l space n u m b e r space i s space i n c o r r e c t. rightwards double arrow 2 minus square root of 3 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 Expert 20th April 2015, 6:09 PM
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