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:

cube of numbers are given below.

Step-by-step explanation:

3n+2

which means 5,8,11, are as follows

1. 5 = 125
2. 8 = 512
3. 11 = 1331

• now the cube of a odd natural number is in the form of3n+2 because
• let a be an natural number and b is an positive natural number, then we get
• a=bq+r
• a = 3n +2 here remainder is 2 so the possible values for the remainder is 1 or
• if remainder is 1 then a =3n +1
• if remainder is 2 then a =3n +2 which is not divisible by 2
• hence

Answer 2

Answer:

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

3 × 1 +2 = 3 + 2 = 5

3 × 2 +2 = 6 + 2 = 8

3 × 3 +2 = 9 + 2 = 11

3 × 4 +2 = 12 + 2 = 14

3 × 5 +2 = 15 + 2 = 17

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

(5)³ = 5 × 5 × 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 +2

512 = 3 × 170 +2

1331 = 3 × 443 +2

2744 = 3 × 914 +2

4971 = 3 × 1637 +2

The cube of a natural number of the form 3n +2 is a natural number of the same factor.

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