Question

So sánh

a/ \(\sqrt{2}\) + \(\sqrt{3}\) và 2

b/ \(\sqrt{3}\) - 5 và -2

Answer 1

a) Ta có: \(\left(\sqrt{2}+\sqrt{3}\right)^2\)

\(=2+2\cdot\sqrt{2}\cdot\sqrt{3}+3\)

\(=5+2\sqrt{6}\)

\(=4+1+2\sqrt{6}>4=2^2\)

\(\Leftrightarrow\left(\sqrt{2}+\sqrt{3}\right)^2>2^2\)

hay \(\sqrt{2}+\sqrt{3}>2\)

Answer 2

b) Ta có: \(\left(\sqrt{3}-5\right)^2=3-2\cdot\sqrt{3}\cdot5+25\)

\(=28-10\sqrt{3}=4+24-10\sqrt{3}>4+0=\left(-2\right)^2\)

\(\Leftrightarrow\sqrt{3}-5>-2\)