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’

Question

Write the cubes 5 natural numbers of the from 3n+2(i.e.5,8,11&#x2026;.) and verify the following: &#x201C;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&#x2019;

Philoid · Accepted 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.

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’

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’