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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

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