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A very large number x is equal to $2^2 \cdot 3^3 \cdot 4^4 \cdot 5^5 \cdot 6^6$. What is the smallest positive integer that, when multiplied with x, produces a product that is a perfect square?

 Jun 21, 2021
 #1
avatar+145 
+2

Here is a question that look similar

https://web2.0calc.com/questions/help-please-asap_31

 

I hope this helps!

 Jun 21, 2021
 #2
avatar+121000 
+1

2^2  *  3^3  * 4^4  *  5^5  *  6^6      =

 

2^2  *  3^3  *  (2^2)^4   *  5^5  *  2^6  * 3^6   =

 

2^2  *  3^3  *  2^8  *  5^5  *  2^6  * 3^6    =

 

2^16  *  3^9  *  5^5

 

We  need  3 *  5   =  15

 

 

cool cool cool

 Jun 21, 2021

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