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How many positive integers n   with  \(n\le 500\)   have square roots that can be expressed in the form  a√b   where a  and b are integers with a\(\ge\)10  ?

 Feb 16, 2019
 #1
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Sorry, misread it.

 Feb 16, 2019
edited by Guest  Feb 16, 2019
edited by Guest  Feb 16, 2019
 #2
avatar+101872 
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I get this many  :

 

sqrt (n) =  a*sqrt(b) with   a ≥ 10

 

sqrt (100) =  10sqrt (1)

sqrt (200) = 10sqrt(2)

sqrt (300) = 10sqrt (3)

sqrt (400) = 10sqrt (4)  or   20sqrt(1)

sqrt (500) = 10sqrt(5)

 

sqrt (121) = 11sqrt(1)

sqrt (242) = 11sqrt(2)

sqrt(363) = 11sqrt(3)

sqrt (484) = 11sqrt(4)   or    22sqrt(1)

 

sqrt ( 144) = 12sqrt (1)

sqrt (288) = 12sqrt(2)

sqrt (432) = 12 sqrt (3)

 

sqrt (169) =  13 sqrt (1)

sqrt (338) = 13sqrt(2)

 

sqrt (196) = 14sqrt(1)

sqrt (392) = 14sqrt (2)

 

sqrt(225) = 15sqrt (1)

sqrt (450) = 15sqrt(2)

 

sqrt  (256) = 16sqrt(1)

 

sqrt (289) = 17sqrt (1)

 

sqrt ( 324) = 18sqrt(1)

 

sqrt(361) = 19sqrt(1)

 

sqrt (441) = 21sqrt(1)

 

 

 

 

cool cool cool

 Feb 16, 2019

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