Question

Write the cubes of 5 natural numbers which are of the form 3n + 2 (e.g., 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.'​

Answer 1

Answer:

The required 5 natural numbers which should be in the given form, namely, 3n + 2 (e.g 5, 8, 11 , …) are as follows:

3 ൱ + 2 = 3 + 2 = 53 ൲ + 2 = 6 + 2 = 83 ൳ + 2 = 9 + 2 = 113 × 4 + 2 = 12 + 2= 143 ൵ + 2 = 15 + 2 = 17

The cubes of the 5 natural numbers which are of the form 3n + 2 (e.g 5, 8, 11, …) are as follows:

(5)3 = 5 ൵ × 5 = 125

(8)3 = 8 × 8 × 8 = 512

(11)3 = 11 × 11 × 11 = 1331

(14)3 = 14 × 14 × 14 = 2744

(17)3 = 17 × 17 × 17 = 4913

Verification:125 = 3 × 41 + 2512 = 3 × 170 + 21331

= 3 × 443 + 22744

= 3 × 914 + 24913

= 3 × 1637 + 2

Therefore, it is verified that the cube of a natural number of the form 3n + 2 is a natural number of the same form'.