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What is the smallest number which 42000 must be multiplied for the result to be a square number?
Wiki User
∙ 11y ago
Let's call this number b
42000 = 24 x 3 x 53 x 7
We have 42000 x b = a2 and a is an integer
Then a = sqrt(42000 x b) = sqrt(b) x sqrt(24 x 3 x 53 x 7)
sqrt(24 x 3 x 53 x 7) = 22 x sqrt(3) x 5 x sqrt(5) x sqrt(7)
For a to be an integer sqrt(b) must be sqrt(3) x sqrt(5) x sqrt(7) at least
Thus b = 105
Wiki User
∙ 11y ago
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