Question

Write the cube of all natural numbers between 1 and 20 and verify the following statement. If the statement is true then the answer is 1 else it is 0.
Statement: Cubes of all even natural numbers are even.

Answer 1

Hint: In this question, we will first multiply the natural number by itself three times to find the cube. Then we will check if the cubes of even natural numbers are even or not. If all of them are even, the statement will be verified.

Complete step-by-step solution -
The cubes of the first three natural numbers are-
$1^3 = 1$
$2^3 = 8$
$3^3 = 27$
$4^3 = 64$
$5^3 = 125$
$6^3 = 216$
$7^3 = 343$
$8^3 = 512$
$9^3 = 729 $
${10}^3 = 1000 $
${11}^3 = 1331 $
${12}^3 = 1728 $
${13}^3 = 2197 $
${14}^3 = 2744 $
${15}^3 = 3375 $
${16}^3 = 4096 $
${17}^3 = 4913 $
${18}^3 = 5832 $
${19}^3 = 6859 $
${20}^3 = 8000 $

The even natural numbers are 2, 4, 6, … 20. The cubes of these natural numbers are 8, 64, 216, … 8000. Hence, we can clearly see that all the cubes are even. Hence, the statement given is true.
Hence, the answer is 1.

Note: Instead of actually calculation the cubes, we can use the properties of even numbers in this problem. When two even numbers are multiplied then their product is also even. While finding the cube of an even number, we are multiplying the same number. Hence, the product will always be even.