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

1.	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.
Answer» 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.

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.

Answer»

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.