Login

pls explain the cube root of 134217728 by estimation method

$T o f i n d t h e c u b e r o o t o f 134217728 b y e s t i m a t i o n m e t h o d, w e h a v e, (1) G r o u p t h e 3 d i g i t s, s t a r t i n g f r o m r i g h t t o l e f t . i . e ., 134 / 217 / 728 (2) \sin c e t h e r e a r e t h r e e g r o u p s o t h e c u b e r o o t w i l l h a v e t h r e e d i g i t s . (3) S i n c e 134 l i e s b e t w e e n 125 a n d 216 i . e ., 5^{3} a n d 6^{3}, t h e r e f o r e t h e s m a l l e r o f t h e s e t w o w i l l b e t a k e n t h a t i s 5 (s o f i r s t d i g i t w i l l b e 5) (4) t h e l a s t d i g i t o f c u b e r o o t i s d e c i d e d b y l a s t g r o u p, i . e ., 728, w h i c h i s e n d i n g b y 8 i t m e a n s c u b e r o o t e n d i n g i n 2 (b e c a u s e 8^{3} = 512, a n d u n i t d i g i t i s 2) (5) N o w, T o f i n d \sec o n d d i g i t, w e h a v e, 5 \times 5 \times 5 = 125 s u b t r a c t 125 f r o m 134 / 217 / 728, w e g e t 134 / 217 / 603 A n d, (f i r s t d i g i t) \times (l a s t d i g i t) \times (l a s t d i g i t) \times (\sec o n d d i g i t) = 5 \times 5 \times 5 \times (\sec o n d d i g i t) = 125 \times \sec o n d d i g i t t h e l a s t d i g i t a t e x t r e m e r i g h t i s 5, w h i c h c a n b e g e t o n l y w h e n \sec o n d d i g i t = 1 T h u s, c u b e r o o t w i l l b e 512.$

-5

View Full Answer

Copyright © 2024 Aakash EduTech Pvt. Ltd. All rights reserved.

Aakash EduTech Pvt. Ltd.

What are you looking for?