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What is the smallest positive integer n such that 3n is a perfect square and 2n is a perfect cube?

 Apr 7, 2020

Best Answer 

 #2
avatar+4569 
+1

We need at least two three's and three two's...

 

We have to add one more three and two more two..

 However, 2*3*2*2 is not a perfect cube but 3*3*2*2

 

We need three  3's and two 2's..

 

3^3*2^2=27*4=108-smallest positive integer.

 Apr 7, 2020
 #1
avatar+252 
+1

Im pretty sure its 108...

 

EDITED FROM MISTAKE

 Apr 7, 2020
edited by MooMooooMooM  Apr 7, 2020
 #2
avatar+4569 
+1
Best Answer

We need at least two three's and three two's...

 

We have to add one more three and two more two..

 However, 2*3*2*2 is not a perfect cube but 3*3*2*2

 

We need three  3's and two 2's..

 

3^3*2^2=27*4=108-smallest positive integer.

tertre Apr 7, 2020

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