kingpinmooski kingpinmooski

21-03-2019
Mathematics

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Find the smallest positive integer such that the product of this integer and 180 is a perfect square.

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LammettHash LammettHash

21-03-2019

Consider the prime factorization of 180:

[tex]180=2^4\cdot5[/tex]

[tex]2^4=(2^2)^2[/tex], so you need to multiply by 5 to get another squared factor.

[tex]180\cdot5=2^4\cdot5^2=(2^2\cdot5)^2[/tex]

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