Question

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

Answer 1

Step 1: Write the cube of natural numbers between $1$ and $10$

Cube of all natural numbers between $1$ and $10$ are as follow:

$2^3=2\times 2\times 2=8$
$3^3=3\times 3\times 3=27$
$4^3=4\times 4\times 4=64$
$5^3=5\times 5\times 5=125$
$6^3=6\times 6\times 6=216$
$7^3=7\times 7\times 7=343$
$8^3=8\times 8\times 8=512$
$9^3=9\times 9\times 9=729$

Step 2: Verify the statement

Statement: Cubes of all odd natural numbers are odd
As, $3^3=27,5^3=125,7^3=343,9^3=729$

From the above result, we can say that cubes of all odd natural numbers are odd.

Hence, the given statement is verified.