# Write the cubes of 5 natural numbers which are multiples of 3 and verify the followings: 'The cube of a natural number which is a multiple of 3 is a multiple of 27' - Mathematics

Sum

Write the cubes of 5 natural numbers which are multiples of 3 and verify the followings:
'The cube of a natural number which is a multiple of 3 is a multiple of 27'

#### Solution

Five natural numbers, which are multiples of 3, are 3, 6, 9, 12 and 15.
Cubes of these five numbers are:

$3^3 = 3 \times 3 \times 3 = 27$

$6^3 = 6 \times 6 \times 6 = 216$

$9^3 = 9 \times 9 \times 9 = 729$

${12}^3 = 12 \times 12 \times 12 = 1728$

${15}^3 = 15 \times 15 \times 15 = 3375$

Now, let us write the cubes as a multiple of 27. We have:

$27 = 27 \times 1$

$216 = 27 \times 8$

$729 = 27 \times 27$

$1728 = 27 \times 64$

$3375 = 27 \times 125$

It is evident that the cubes of the above multiples of 3 could be written as multiples of 27. Thus, it is verified that the cube of a natural number, which is a multiple of 3, is a multiple of 27.

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 4 Cubes and Cube Roots
Exercise 4.1 | Q 4 | Page 8