represent 2-root 3 on number line

Asked by nisha_vini29 | 28th Apr, 2015, 09:17: AM

Expert Answer:

S t e p space 1 colon D r a w space a space l i n e space a n d space m a r k space a space p o i n t space A space s u c h space t h a t space O A equals 1 space u n i t s. S t e p space 2 colon space M a r k space p o i n t s space B space a n d space C space s u c h space t h a t comma space A B equals B C equals 1 space u n i t. S t e p space 3 colon space D r a w space C D perpendicular O B space s u c h space t h a t space C D equals 1 S t e p space 4 colon space J o i n space B D. T h u s comma space i n space r i g h t space t r i a n g l e space B C D comma B y space P y t h a g o r a s space T h e o r e m comma space w e space h a v e comma B D squared equals B C squared plus C D squared space space space space space space equals 1 squared plus 1 squared space space space space space space equals 2 rightwards double arrow B D equals square root of 2 space u n i t s.  S t e p space 5 colon space D r a w space D E perpendicular B D space s u c h space t h a t space D E equals 1 space u n i t. A g a i n comma space i n space r i g h t space t r i a n g l e space B D E comma B y space P y t h a g o r a s space T h e o r e m comma space w e space h a v e comma B E squared equals B D squared plus D E squared space space space space space space equals open parentheses square root of 2 close parentheses squared plus 1 squared space space space space space space equals 3 rightwards double arrow B E equals square root of 3 space u n i t s. S t e p space 6 colon space W i t h space c e n t r e space a s space B space a n d space r a d i u s equals B E equals square root of 3 space comma space d r a w space a n space a r c space b e t w e e n space O space a n d space B space a t space F. O B equals 2 space u n i t s comma space B E equals square root of 3 space u n i t s space a n d space B F equals square root of 3 space u n i t s T h u s comma space f r o m space t h e space n u m b e r space l i n e space i t space i s space c l e a r space t h a t comma O F equals O B minus B F equals 2 minus square root of 3 space T h e r e f o r e comma space O F space i s space r e q u i r e d space l e n g t h space o f space t h e space i r r a t i o n a l space n u m b e r space 2 minus square root of 3
 

Answered by Vimala Ramamurthy | 28th Apr, 2015, 11:04: AM