what is the simplest way to find the under root if decimal numbers?For example;root of 139.69 .

Asked by sangyaagarwal | 14th Dec, 2015, 05:36: PM

Expert Answer:

C o n s i d e r space t h e space d e c i m a l space n u m b e r space 139.69 S t e p space 1 colon P e r f e c t space s q u a r e s space n e a r space b y space 139.69 space a r e space 121 space a n d space 144 T h a t space i s comma space 11 less than square root of 139.69 end root less than 12 S t e p space 2 colon S i n c e space 139.69 space i s space c l o s e r space t o space 12 space t h a n space 11 comma space l e t space u s space a s s u m e space t h a t space t h e space s q u a r e space r o o t space o f space 139.69 space i s space a p p r o x i m a t e l y space 11.7 S t e p space 3 colon N o w space d i v i d e space 139.69 space b y space 11.7. fraction numerator 139.69 over denominator 11.7 end fraction equals 11.93 S t e p space 4 colon space T a k e space t h e space a v e r a g e space o f space 11.7 space a n d space 11.93 n e w space s q u a r e space r o o t equals fraction numerator 11.7 plus 11.93 over denominator 2 end fraction equals 11.815 S t e p space 5 colon N o w space r e p e a t space t h e space s t e p s space 3 comma space 4 space a n d space 5 space t i l l space y o u space r e a c h space m o s t space a c c u r a t e space s q u a r e space r o o t space o f space t h e space r e q u i r e d space n u m b e r. fraction numerator 139.69 over denominator 11.815 end fraction equals 11.823 fraction numerator 11.815 plus 11.823 over denominator 2 end fraction equals 11.819  T h u s space 11.819 space i s space t h e space a p p r o x i m a t e space s q u a r e space r o o t space o f space 139.69

Answered by Vimala Ramamurthy | 15th Dec, 2015, 09:01: AM