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Grades 11-12 Video Solutions 2022
2022_11-12_27
2022_11-12_27
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Video Transcription
Video Summary
The task is to find the number of integers between two square root expressions: \(\sqrt{n^2 + n + 1}\) and \(\sqrt{9n^2 + n + 1}\). By squaring both expressions, the problem simplifies to finding the number of perfect squares between \((n+1)^2\) and \((3n)^2\). Since the range starts at \((n+1)^2\) and ends at \((3n)^2\), the total count of perfect squares is \(3n - (n+1) + 1 = 2n\). Another approach is comparing results for specific values of \(n\) to confirm the linear relationship of the result. Thus, the answer is \(2n\).
Keywords
square root expressions
perfect squares
integer count
linear relationship
mathematical problem
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