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.

To do:

We have to write the cubes of all natural numbers between 1 and 10 and verify the given statements.

Solution:  

Cubes of first 10 natural numbers are:

$(1)^3=1\times1\times1=1$

$(2)^3=2\times2\times2=8$

$(3)^3=3\times3\times3=27$

$(4)^3=4\times4\times4=64$

$(5)^3=5\times5\times5=125$

$(6)^3=6\times6\times6=216$

$(7)^3=7\times7\times7=343$

$(8)^3=8\times8\times8=512$

$(9)^3=9\times9\times9=729$

$(10)^3=10\times10\times10=1000$

From the above cubes of first 10 natural numbers, 

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

The given statement is true.

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

The given statement is true.

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Updated on: 10-Oct-2022

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