Question

Find the smallest number by which 3200 should be multiplied so that the product is perfect cube

Answer 1

Answer:

3600=3×3×2×2×2×2×5×5

=3

2

×2

4

×5

2

A perfect cube has multiples of 3 as powers of factors.

i.e. the number has to be multiplied by 3×2×2×5=60 to make it a perfect cube.

Answer 2

Answer:

Hence, $20$ is the shortest count to be multiplied with $3200$ in order to give a perfect cube.

Step-by-step explanation:

Concept:

A number can be expressed as a perfect cube by multiplying the same integer three times. The result of multiplying the same integer three times is the perfect cube.

Given:

Count to be multiplied with$= 3200$

To find:

The smallest number multiplied with $3200$ for a perfect cube.

Solution:

Here, we required to find a count which when multiplied with $3200$ should give a perfect cube.

Firstly finding the factors of $3200$,

$3200=2*2*2*2*2*2*2*5*5$

There are two triplets of $2$, one of $2$ and two $5$ are left.

So when we complete the incomplete triplets we get the prefect cube.

To complete the triplets we have to multiply it with a pair of $2$ and with one $5$.

$=2*2*5\\=20$

Thus, when we multiply $3200$ with $20$,  the resultant will be $64000$ which is a perfect cube.

Hence, $20$ is the shortest count to be multiplied with $3200$ in order to give a perfect cube.

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