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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’ |
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Answer» As we know that the first 5 natural numbers in the form (3n + 2) are 5, 8, 11, 14 and 17 The cubes of 5, 8, 11, 14 and 17 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 All these cubes when divided by ‘3’ leaves remainder 2. \(\therefore\) “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’ is true. |
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