Question

So sánh 2+\(\sqrt{2}\) và 5-\(\sqrt{3}\)

Answer 1

Ta có: \(\left(2+\sqrt{2}\right)^2\)

\(=4+4\sqrt{2}+2\)

\(=6+4\sqrt{2}\simeq11,66\)

Ta có: \(\left(5-\sqrt{3}\right)^2\)

\(=25-10\sqrt{3}+3\)

\(=28-10\sqrt{3}\simeq10,68\)

mà 11,66>10,68

nên \(2+\sqrt{2}>5-\sqrt{3}\)

Answer 2

\(2+\sqrt{2}=2+\sqrt{\frac{200}{100}}>2+\sqrt{\frac{169}{100}}=\frac{33}{10}\)

\(5-\sqrt{3}=5-\sqrt{\frac{300}{100}}< 5-\sqrt{\frac{289}{100}}=\frac{33}{10}\)

\(\Rightarrow2+\sqrt{2}>5-\sqrt{3}\)