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A very large number x is equal to \(2^23^34^45^56^67^78^89^9\). What is the smallest positive integer that, when multiplied with x, produces a product that is a perfect square?

Thank You So Much!!!

 Oct 12, 2020
 #2
avatar+111124 
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Hint:    All the indices must be even numbers.

 
 Oct 12, 2020
 #3
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Except 9^9 = 3^18

 
 Oct 13, 2020
 #4
avatar+111124 
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Yes you are right,

 

I will tweak my answer.

 

All the factors must be prime  THEN all the indices of these prme factors must by even.

 

So with your example. 

 

\(9^9=(3^2)^9=3^{18}\\ \text{18 is even so } 9^9 \text { is a square number}\)

 
Melody  Oct 13, 2020

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