Q. 6

Write the cubes 5 natural numbers of the from 3n+2(i.e.5,8,11….) and verify the following:

“The cube of a natural number of the form 3n+2 is a natural number of the same form i. e. when it is dividend by 3 the remainder is 2’

Answer :

First 5 natural numbers in form ( 3n + 2 ) are = 5 , 8 , 11 , 14 , 17


Cubes of these numbers are,


= 53 = 5 × 5 × 5 = 125


= 83 = 8 × 8 × 8 = 512


= 113 = 11 × 11 × 11 = 1331


= 143 = 14 × 14 × 14 = 2744


= 173 = 17 × 17 × 17 = 4313


We find that all these cubes give remainder 2 when divided by 3..


Hence statement is true.


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