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A number that is both a perfect square and perfect cube and six digits long (whole positive number), what is this number?

I need help!

 Jan 15, 2017

Best Answer 

 #2
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+5

OK, young person. I got your number:

531,441 =729^2

531,441 =81^3

 Jan 15, 2017
 #1
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0

1,000,000 =1,000^2

1,000,000 =100^3

I know you said "6-digits long", but this is 7-digits long!.

 Jan 15, 2017
 #2
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+5
Best Answer

OK, young person. I got your number:

531,441 =729^2

531,441 =81^3

Guest Jan 15, 2017
 #3
avatar+129839 
+5

"Guest's "  answer isn't unique.....for example......

 

117649  = 343^2

117649 =    49^3

 

262144  = 512^2

262144  = 64^3

 

I suspect that, integer-wise, this may be all

 

[ 6 * 6 ] ^3   = [36]^3   = 46.656  ..... too small

[ 7 * 7 ] ^3 =   [49]^3  = 117649

[8 * 8 ] ^3  =   [64]^3  = 262144

[9 * 9 ] ^3  =   [81]^3  =  531441

[ 10 * 10] ^3  = [100]^3  = 1,000,000  ...... too large

 

 

 

 

cool cool cool

 Jan 15, 2017

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