Question

Write cubes of 4 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'. [4 MARKS]

Answer 1

Concept:1 Mark
Application: 2 Marks
Verification: 1 Mark

The 4 natural numbers which are of the form 3n + 2 (e.g 5, 8, 11, .....) are as follows:

$3\times 1+2=3+2=5$

$3\times 2+2=6+2=8$

$3\times 3+2=9+2=11$

$3\times 4+2=12+2=14$

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

$(5{)}^3=5\times 5\times 5=125$

$(8{)}^3=8\times 8\times 8=512$

$(11{)}^3=11\times 11\times 11=1331$

$(14{)}^3=14\times 14\times 14=2744$


Verification:

$125=3\times 41+2$

$512=3\times 170+2$

$1331=3\times 443+2$

$2744=3\times 914+2$

$\therefore$ 'The cube of a natural number of the form 3n + 2 is a natural number of the same form