Challenge:
What is the smallest positive integer p such that 1080p is a perfect cube number?
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The correct answer is 25.
First, find the factor of 1080p. The prime factors of 1080p are:
\(2^3×3^3×5×p\)
In order for \(2^3×3^3×5×p\) to be a perfect cube, each prime factor must come in sets of triples. Since, we have \(2^3×3^3×5\), thus, we only need to change 5 to \(5^3\). Therefore, p equals to \(5^2\) or 25.
Reza is an experienced Math instructor and a test-prep expert who has been tutoring students since 2008. He has helped many students raise their standardized test scores--and attend the colleges of their dreams. He works with students individually and in group settings, he tutors both live and online Math courses and the Math portion of standardized tests. He provides an individualized custom learning plan and the personalized attention that makes a difference in how students view math.
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