Question

Bài tập: So sánh
1) \(\dfrac{1}{3}\sqrt{51}\) và \(\dfrac{1}{5}\sqrt{150}\)

2) \(\dfrac{1}{2}\sqrt{6}\) và \(6\sqrt{\dfrac{1}{2}}\)

Answer 1

1,

1\(1,\dfrac{1}{3}\sqrt{51}=\dfrac{\sqrt{51}}{3}\\ \dfrac{1}{5}\sqrt{150}=\sqrt{6}\)

\(\dfrac{\sqrt{51}}{3};\sqrt{6}=\dfrac{3\sqrt{6}}{3}=\dfrac{\sqrt{54}}{3}\)

\(51< 54=>\dfrac{1}{3}\sqrt{51}< \dfrac{1}{5}\sqrt{150}\)

2, 

\(\dfrac{1}{2}\sqrt{6}=\sqrt{\dfrac{1}{4}.6}=\sqrt{\dfrac{3}{2}}=\dfrac{\sqrt{6}}{2}\\ 6\sqrt{\dfrac{1}{2}}=\sqrt{\dfrac{36.1}{2}}=\sqrt{18}=3\sqrt{2}\)

\(\dfrac{\sqrt{6}}{2};3\sqrt{2}=\dfrac{2.3\sqrt{2}}{2}=\dfrac{6\sqrt{2}}{2}=\dfrac{\sqrt{72}}{2}\\ \sqrt{6}< \sqrt{72}=>\dfrac{1}{2}\sqrt{6}< 6\sqrt{\dfrac{1}{2}}\)

Answer 2

1) Có: \(\dfrac{1}{3}\sqrt{51}>\dfrac{1}{3}\sqrt{50}=\dfrac{1}{3}.\sqrt{5}\sqrt{10}=\dfrac{\sqrt{5}}{3}\sqrt{10}\)

\(\dfrac{1}{5}\sqrt{150}=\dfrac{1}{5}.\sqrt{15}\sqrt{10}=\dfrac{\sqrt{15}}{5}\sqrt{10}=\dfrac{\sqrt{3}\sqrt{5}}{\sqrt{5}\sqrt{5}}\sqrt{10}=\sqrt{\dfrac{3}{5}}\sqrt{10}< \dfrac{\sqrt{5}}{3}\sqrt{10}=\dfrac{1}{3}\sqrt{51}\)

2) Có: \(\dfrac{1}{2}\sqrt{6}=\dfrac{\sqrt{6}}{\sqrt{2}\sqrt{2}}=\dfrac{\sqrt{2}\sqrt{3}}{\sqrt{2}\sqrt{2}}=\dfrac{\sqrt{3}}{\sqrt{2}}=\sqrt{\dfrac{3}{2}}\)

\(6\sqrt{\dfrac{1}{2}}=\dfrac{6.1}{\sqrt{2}}=\dfrac{\sqrt{2}\sqrt{2}.3}{\sqrt{2}}=\sqrt{2}.3>\sqrt{\dfrac{3}{2}}=\dfrac{1}{2}\sqrt{6}\)