Question

find the smallest number which when multiplied with 3600 will make the product a perfect cube . Further, find the cube root of the product
solve it step by step
ans will be-60,60

Answer 1

Hey

Here is your answer,

On factorising 3600 into prime factors, we get:
3600=2×2×2×2×3×3×5×5

On grouping the factors in triples of equal factors, we get:
3600=2×2×2×2×3×3×5×5

It is evident that the prime factors of 3600 cannot be grouped into triples of equal factors such that no factor is left over.
Therefore, 3600 is not a perfect cube.
However, if the number is multiplied by (2×2×3×5=60), the factors can be grouped into triples of equal factors such that no factor is left over.

Hence, the number 3600 should be multiplied by 60 to make it a perfect cube.

Also, the product is given as:

3600×60=2×2×2×2×3×3×5×5×60⇒216000=2×2×2×2×3×3×5×5×2×2×3×5⇒216000=2×2×2×2×2×2×3×3×3×5×5×5

To get the cube root of the produce 216000, take one factor from each triple.

Cube root = 2×2×3×5=60

Hence, the required numbers are 60 and 60.

Hope it helps you!

Answer 2

Hello Dear!!!!

Here's your answer...

The given number is 3600

First,we have to do prime factorization

3600 = 3*3*2*2*2*2*5*5

3600 = 3^2 * 2^4 * 5^2

To become a cube...the powers should be equal to multiple of 3

the power of 3 is 2

The power of 2 is 4

The power of 5 is 2

so...we need to multply one 3...two 2's and one 5

so...

3*2*2*5

60

3600 should be multiplied with 60 to become cube..

3600*60

216000

so...

∛21600

60

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HOPE THIS HELPS YOU...