Question

So sánh:(Không sử dụng máy tính )

a)\(\frac{1}{3}\sqrt{51}\)và \(\frac{1}{5}\sqrt{150}\)

b)\(\frac{1}{2}\sqrt{6}\)và \(6\sqrt{\frac{1}{2}}\)

Answer 1

a) Ta có: \(\frac{1}{5}\sqrt{150}=\frac{1}{5}\cdot5\sqrt{6}=\sqrt{6}=\frac{1}{3}\cdot\sqrt{6\cdot9}=\frac{1}{3}\sqrt{54}>\frac{1}{3}\sqrt{51}\)

b) Ta có: \(\frac{1}{2}\sqrt{6}=\sqrt{\frac{6}{4}}< \sqrt{\frac{36}{2}}=6\sqrt{\frac{1}{2}}\)

Answer 2

a) Vì  \(5,\left(6\right)< 6\)\(\Rightarrow\)\(\frac{51}{9}< \frac{150}{25}\)

                                    \(\Rightarrow\)\(\sqrt{\frac{51}{9}}< \sqrt{\frac{150}{25}}\)

                                    \(\Rightarrow\)\(\frac{1}{3}\sqrt{51}< \frac{1}{5}\sqrt{150}\)

b) Vì  \(1,5< 18\)\(\Rightarrow\)\(\frac{6}{4}< \frac{36}{2}\)

                                 \(\Rightarrow\)\(\sqrt{\frac{6}{4}}< \sqrt{\frac{36}{2}}\)

                                 \(\Rightarrow\)\(\frac{1}{2}\sqrt{6}< 6\sqrt{\frac{1}{2}}\)