how to represent root 10.5 on the number line by not using geomtrical costruction ?

Asked by iamprets3011 | 22nd Sep, 2015, 04:48: PM

Expert Answer:

T h e space m e t h o d s space o f space f i n d i n g space a space S q u a r e space r o o t space o f space a space n u m b e r space w h i c h space i s space n o t space a space p e r f e c t space s q u a r e space a r e colon 1. space G e o m e t r i c a l space c o n s t r u c t i o n 2. space L o n g space d i v i s i o n space m e t h o d 3. space E s t i m a t i o n space m e t h o d. 4. space V e d i c space m a t h e m c a t i c s.  N o w space l e t space u s space s e e space e s t i m a t i o n space m e t h o d colon S t e p 1 colon space T h e space g i v e n space n u m b e r comma space 10.5 space l i e s space b e t w e e n space 9 space a n d space 16 T h a t space i s comma space 9 less than 10.5 less than 16 rightwards double arrow square root of 9 less than square root of 10.5 end root less than square root of 16 rightwards double arrow 3 less than square root of 10.5 end root less than 4 S t e p space 2 colon space D i v i d e space t h e space n u m b e r space 10.5 space b y space 3 space o r space 4 T h u s comma space fraction numerator 10.5 over denominator 3 end fraction equals 3.5 S t e p space 3 colon space T a k e space t h e space a v e r a g e space o f space 3 space a n d space 3.5 T h u s comma space fraction numerator 3 plus 3.5 over denominator 2 end fraction equals 3.25 S t e p space 4 colon space C h e c k space w h e t h e r space open parentheses 3.25 close parentheses squared almost equal to 10.5 I f space n o t space r e p e a t space t h e space c y c l e space o f space s t e p s space f r o m space s t e p space 2. S t e p space 2 colon T h u s comma space fraction numerator 10.5 over denominator 3.25 end fraction almost equal to 3.23 S t e p space 3 colon space T a k e space t h e space a v e r a g e space o f space 3.23 space a n d space 3.25 fraction numerator 3.23 plus 3.25 over denominator 2 end fraction equals 3.24 S t e p space 4 colon space open parentheses 3.24 close parentheses squared almost equal to 10.4976 T h u s comma space s q u a r e space r o o t space o f space 10.5 space i s space a p p r o x i m a t e l y space e q u a l space t o space 3.24 left parenthesis r o u n d e d space o f f space t o space t w o space d e c i m a l space p l a c e s right parenthesis. N o w space w e space c a n space p l o t space 3.24 space o n space t h e space n u m b e r space l i n e space b y space d i v i d i n g space o n e space t i c k space u n i t s space i n t o space 100 space u n i t s space f r o m space 3 space t o space 4 space a n d space m a r k space t h 24 t h space p o s i t i o n space f r o m space 3.

Answered by Vimala Ramamurthy | 23rd Sep, 2015, 10:09: AM