What is the increasing order of (\sqrt{1}), (\sqrt{2}), and (\sqrt{3}) on the number line?

Correct answer: (\sqrt{1},\sqrt{2},\sqrt{3})

The direct answer is option B: \(\sqrt{1},\sqrt{2},\sqrt{3}\). For non-negative numbers, the square-root function preserves order: if \(1<2<3\), then \(\sqrt{1}<\sqrt{2}<\sqrt{3}\). We may also evaluate them: \(\sqrt{1}=1\), \(\sqrt{2}\approx1.414\), and \(\sqrt{3}\approx1.732\). Therefore they appear from left to right in the stated order. Option A reverses the order, so it is decreasing rather than increasing. Option B follows the increasing order and is correct. Option C places \(\sqrt{2}\) before \(\sqrt{1}\), which is impossible because \(\sqrt{2}>1\). Option D puts \(\sqrt{3}\) before \(\sqrt{2}\), although \(\sqrt{3}>\sqrt{2}\). The useful rule is to compare the non-negative numbers inside the roots; larger radicand gives larger square root.