Question

So sánh:

\(A=\sqrt{2}+\sqrt{6}+\sqrt{12}+\sqrt{20}+\sqrt{30}+\sqrt{42}\)

B=24

Answer 1

\(\sqrt{2}=\sqrt{1.2}< \dfrac{\left(1+2\right)}{2}=\dfrac{3}{2}\)

\(\sqrt{6}=\sqrt{2.3}< \dfrac{\left(2+3\right)}{2}=\dfrac{5}{2}\)

\(\sqrt{12}=\sqrt{3.4}< \dfrac{3+4}{2}=\dfrac{7}{2}\)

\(\sqrt{20}=\sqrt{4.5}< \dfrac{4+5}{2}=\dfrac{9}{2}\)

\(\sqrt{30}=\sqrt{5.6}< \dfrac{5+6}{2}=\dfrac{11}{2}\)

\(\sqrt{42}=\sqrt{6.7}< \dfrac{6+7}{2}=\dfrac{13}{2}\)

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VT \(VT=A< \dfrac{3+5+7+9+11+13}{2}=\dfrac{48}{2}=24=VP=B\)