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\(Find the number of positive integers $n$ so that \[4 < \sqrt{n} < 10.\]\)

 Apr 20, 2019

You know that \(\sqrt{16}=4\) and \(\sqrt{100}=10\) so you need to find how many numbers in 17,18,19....99

My way of doing this is just making the first number 1 and the last number is the number of numbers in the set. So you need to subtract 16 from all the numbers to make the first one 1. The set becomes 1,2,3....83. Therefore there is 83 positive integers that satisfy the inequality.

 Apr 20, 2019

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