If \(a\) and \(b\) are both positive integers such that \(a < b,\) which of the following must be true?

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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