Q2 of 76 Page 5

Write the cubes of all natural numbers between 1 and 10 and verify the following statements:

(i) Cubes of all odd natural numbers are odd.


(ii) Cubes of all even natural numbers are even.

Cube of natural numbers upto 10 are as follows.


13 = 1 × 1 × 1 = 1


23 = 2 × 2 × 2 = 8


33 = 3 × 3 × 3 = 27


43 = 4 × 4 × 4 = 64


53 = 5 × 5 × 5 = 125


63 = 6 × 6 × 6 = 216


73 = 7 × 7 × 7 = 343


83 = 8 × 8 × 8 = 512


93 = 9 × 9 × 9 = 729


103 = 10 × 10 × 10 = 1000


From above results we can see that,


(i) Cubes of all odd natural numbers are odd.


(ii) Cubes of all even natural numbers are even.


More from this chapter

All 76 →
1

Find the cubes of the following numbers:

(i) 7 (ii) 12


(iii) 16 (iv) 21


(v) 40 (vi) 55


(vii) 100 (viii) 302


(ix) 301

 3

Observe the following pattern:


Write the next three rows and calculate the value of by the above pattern.

 4

Write the cubes of 5 natural numbers which are multiples of 3 and verify the followings:

“The cube of a natural number which is a multiple of 3 is a multiple of 27’

 5

Write the cubes of 5 natural numbers which are of the form and verify the following:

“The cube of a natural number of the form 3n+1 is a natural number of the same from i.e. when divided by 3 it leaves the remainder 1’