Write the cubes of 5 natural numbers which are multiples of 3 and verify the following: The cube of a natural number which is a multiple of 3 is a multiple of 27.
Given:
The cube of a natural number which is a multiple of 3 is a multiple of 27.
To do:
We have to write the cubes of 5 natural numbers which are multiples of 3 and verify the given statement.
Solution:
First 5 natural numbers which are multiples of 3 are $3,6,9,12,15$.
Therefore,
$(3)^3=3\times3\times3=27$
$=27\times1$
$(6)^3=6\times6\times6=216$
$=27\times8$
$(9)^3=9\times9\times9=729$
$=27\times27$
$(12)^3=12\times12\times12=1728$
$=27\times64$
$(15)^3=15\times15\times15=3375$
$=27\times125$
$27, 216, 729, 1728, 3375$ are multiples of 27.
Hence, the given statement is true.
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