For how many different positive integers n does sqrt(n) differ from sqrt(100) by less than 1?
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The difference between √81 and √100 is 1. The difference between √121 and √100 is also 1. So, the integers in the interval (81, 121) satisfy the requirement.
So, n = 39
Mark M. answered • 08/05/19
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√n - √100 < 1
√n < 1 + √100
n < 1 + 2√100 + 100
n < 1 + 20 + 100
n < 121
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Mark M.
The question is ambiguous. Do you want the difference to be less than one, i.e., x - y < 1, or do you want the squares roots to differ by less than one?08/05/19