find the smallest number when multiplied with 3600 will make the product a perfect cube further find the cube root of the product
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not sure if theres an actual way to go about this.
But, 3600 is the square of 60
Therefore if 60 were to be multiplied into 3600 the product would be a perfect cube of cube root 60.
But is 60 the smallest no.?
Prime factors of 60: 3, 5, 2, 2
Therefore in 3600 (which is 60 x 60) we have (3*5*2*2)x(3*5*2*2)
Now using factorisation method to check if a number is a perfect cube, we check if the factors can be grouped into sets of three. Applying the same logic, We need atleast another 3, another 5, and two more 2's, for the factors of the product of 3600 and the mystery no. to be grouped into sets of three.
Therefore 3*5*2*2=60
So 60 really is the smallest no.
This is the logical way to go about, if there is a mechanical one, I am not aware of it.
Hope this helps. :)
But, 3600 is the square of 60
Therefore if 60 were to be multiplied into 3600 the product would be a perfect cube of cube root 60.
But is 60 the smallest no.?
Prime factors of 60: 3, 5, 2, 2
Therefore in 3600 (which is 60 x 60) we have (3*5*2*2)x(3*5*2*2)
Now using factorisation method to check if a number is a perfect cube, we check if the factors can be grouped into sets of three. Applying the same logic, We need atleast another 3, another 5, and two more 2's, for the factors of the product of 3600 and the mystery no. to be grouped into sets of three.
Therefore 3*5*2*2=60
So 60 really is the smallest no.
This is the logical way to go about, if there is a mechanical one, I am not aware of it.
Hope this helps. :)
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