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

 Feb 17, 2019
 #1
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There are 23 such numbers as follows:

(100, 121, 144, 169, 196, 200, 225, 242, 256, 288, 289, 300, 324, 338, 361, 363, 392, 400, 432, 441, 450, 484, 500) =23 such numbers.

You can write each number as: 100 =10sqrt(1), 200 =10Sqrt(2), 288=12sqrt(2)......and so on.

 Feb 17, 2019
 #2
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Thank you

 Feb 17, 2019

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