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If \(a\) and \(b\) are both positive integers such that \(a < b,\) which of the following must be true?
(A) \(a<\sqrt{ab}<b\)
(B) \(\sqrt{a}<\sqrt{ab}<\sqrt{b}\)
(C) \(\sqrt{a}<\sqrt{b}<\sqrt{ab}\)
(D) \(\sqrt{ab}<a<b\)
(D) \(a<\sqrt{ab}<\sqrt{b}\)
Answer: A
Source: Veritas Prep
(A) \(a<\sqrt{ab}<b\)
(B) \(\sqrt{a}<\sqrt{ab}<\sqrt{b}\)
(C) \(\sqrt{a}<\sqrt{b}<\sqrt{ab}\)
(D) \(\sqrt{ab}<a<b\)
(D) \(a<\sqrt{ab}<\sqrt{b}\)
Answer: A
Source: Veritas Prep
