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# what is the smallest positive number P such that 10500P is a perfect cube?

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what is the smallest positive number P such that 10500P is a perfect cube?

Guest Feb 12, 2015

#2
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Sorry Melody, it's 882.

Guest Feb 12, 2015
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#1
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What is the smallest positive number P such that 10500P is a perfect cube?

10500=105*100=7*3*10^2*5

The smallest possible number is\\

7^2*3^2*2

=49*9*2

$${\mathtt{49}}{\mathtt{\,\times\,}}{\mathtt{9}}{\mathtt{\,\times\,}}{\mathtt{2}} = {\mathtt{882}}$$

the smallest number p can be is 882             Corrections made - Thanks anon :)

Melody  Feb 12, 2015
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