can u please show it with an example taking the cube of 105 and getting 105 back after prime factorisation. Thank u i will learn the cubes.

Asked by joshiraghavendra53 | 21st Mar, 2015, 03:03: PM

Expert Answer:

$C u b e space o f space 105 equals 105 cubed space space space space space space space space space space space space space space space space space space space space space equals 105 cross times 105 cross times 105 space space space space space space space space space space space space space space space space space space space space space equals 1157625 N o w space c o n s i d e r space t h e space p r i m e space f a c t o r i z a t i o n space o f space t h e space n u m b e r space 1157625 colon T h u s comma space 1157625 equals 3 cross times 3 cross times 3 cross times 5 cross times 5 cross times 5 cross times 7 cross times 7 cross times 7 rightwards double arrow 1157625 equals 3 cubed cross times 5 cubed cross times 7 cubed rightwards double arrow 1157625 equals open parentheses 3 cross times 5 cross times 7 close parentheses cubed rightwards double arrow 1157625 equals open parentheses 105 close parentheses cubed T h u s comma space c u b e space r o o t space o f space t h e space n u m b e r space 1157625 space i s space 105. space$

Answered by Vimala Ramamurthy | 24th Mar, 2015, 09:02: AM

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