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28 times a 2 digit number is a perfect cube. What is that number

 Apr 17, 2023
 #1
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HELP!!!

 Apr 18, 2023
 #2
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28  x  98 ==2,744

 

2,744^(1/3) ==14

 

So, your 2-digit number is: 98

 Apr 18, 2023
 #3
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Let the answer number be y

the 2 digit number be M

 

\(10\le M\le99\\ 280\le 28M\le 2772\\ 280\le y^3 \le 2772\\ 7\le y \le 14\\ \)

 

So y could be  7, 8, 9, 10, 11, 12, 13, or 14

 

7^3 = 343   and 343 is not divisable by 28 so the answer is not 7

 

Just try all the other numbers to find the one that works.   wink

 Apr 18, 2023
 #4
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28 = 2^2 * 7

 

So, the smallest 2-digit number will be:

 

2^1 x 7^2 ==98

 

So, the perfect cube will be:

 

2^3 x 7^3 =2,744

 Apr 18, 2023

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