Verified answer

Step-by-step explanation:

3. To find the smallest number by which 675 should be multiplied to get a perfect cube, we need to prime factorize 675.

675 = 3 × 3 × 3 × 5 × 5 × 5

To make it a perfect cube, we need to multiply it by the missing prime factors. In this case, we need to multiply it by 3 × 5 × 5 = 75.

So, the smallest number by which 675 should be multiplied to get a perfect cube is 75.

4. To find the smallest number by which 2916 should be divided to get a perfect cube, we need to prime factorize 2916.

2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

To make it a perfect cube, we need to divide it by the repeated prime factors. In this case, we need to divide it by 2 × 3 × 3 = 18.

So, the smallest number by which 2916 should be divided to get a perfect cube is 18.

5. Let's write the cubes of five natural numbers that are multiples of 3:

3³ = 27

6³ = 216

9³ = 729

12³ = 1728

15³ = 3375

Now, let's verify the statement "The cube of a natural number which is a multiple of 3 is a multiple of 27."

If we take any of the numbers we listed above and divide it by 27, we will get a whole number. For example, 216 divided by 27 is 8, and 3375 divided by 27 is 125.

So, the statement "The cube of a natural number which is a multiple of 3 is a multiple of 27" is verified.

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