Problem Solving (PS) | Re: If a and b are integers such that a is the product of

\( a =m*\sqrt{60} = m *2*\sqrt{15}\)

For 'a' to be an integer, 'm' must have another sqrt(15) in it at least.
So 'a' is at least30.

\( b = n *\sqrt{75}\)
\( b = n *5*\sqrt{3}\)

For 'b' to be an integer, 'n' must have another sqrt(3) in it at least.
So 'b' is at least 15.

Hence 'ab' is at least 30*15 = 450
So 90 is certainly a factor of 'ab'.

Answer
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