Question

So sánh:

\(\frac{15-2\sqrt{10}}{3}\) va \(\sqrt{10}\)

Answer 1

Xét A-B=5-\(\sqrt{10}\)(2/3+1)= 5-\(\frac{5\sqrt{10}}{3}\)=5(1-\(\frac{\sqrt{10}}{3}\)) < 0

Vậy A<B

Answer 2

\(2\sqrt{10}=\sqrt{4\cdot10}=\sqrt{40}>\sqrt{36}=6\Rightarrow2\sqrt{10}>6\)

\(\Rightarrow15-2\sqrt{10}< 15-6=9\Rightarrow\frac{15-2\sqrt{10}}{3}< \frac{9}{3}=3\)mà \(3=\sqrt{9}< \sqrt{10}\Rightarrow\frac{15-2\sqrt{10}}{3}< \sqrt{10}\)