Find the  cube root of the following:
1)2744.                                                  2)4913.          
3)Find the smallest number by which 2560 must be multiplied so that the product becomes a perfect cube.
4)Find the smallest number by which 432 must be divided so that the quotient is a perfect cube.
5) The sum of the cubes of three numbers which are in the ratio 1:2:3 is 7776. Find the numbers.
 

Asked by Krishna | 24th Aug, 2015, 12:45: PM

Expert Answer:

begin mathsize 14px style 1. space space space 2744 equals 2 cross times 2 cross times 2 cross times 7 cross times 7 cross times 7 equals 2 cubed cross times 7 cubed equals left parenthesis 2 cross times 7 right parenthesis cubed cube root of 2744 equals 2 cross times 7 equals 14  2. space space space 4913 equals 17 cross times 17 cross times 17 equals 17 cubed cube root of 4913 equals 17 end style
 
begin mathsize 16px style 3. space space space P r i m e space f a c t o r i s a t i o n space o f space 2560 equals bottom enclose 2 cross times 2 cross times 2 end enclose cross times bottom enclose 2 cross times 2 cross times 2 end enclose cross times bottom enclose 2 cross times 2 cross times 2 end enclose cross times 5 H e r e comma space t h e space p r i m e space f a c t o r space 5 space d o e s space n o t space a p p e a r space i n space t h e space g r o u p space o f space 3. space I t space o c c u r s space o n l y space o n c e. T h u s space i n space o r d e r space t o space m a k e space t h e space g i v e n space n u m b e r space a space p e r f e c t space c u b e comma space w e space n e e d space t o space m u l t i p l y space i t space b y space 5 space cross times 5 equals 25. T h u s comma space 2560 cross times 5 cross times 5 equals bottom enclose 2 cross times 2 cross times 2 end enclose cross times bottom enclose 2 cross times 2 cross times 2 end enclose cross times bottom enclose 2 cross times 2 cross times 2 end enclose cross times bottom enclose 5 cross times 5 cross times 5 end enclose end style

Answered by Rashmi Khot | 25th Aug, 2015, 09:11: AM