Question

So sánh:

4 và \(1+2\sqrt{2}\)

4 và \(2\sqrt{6}-1\)

\(\sqrt{0,5}\)và\(\sqrt{3}-2\)

\(-3\sqrt{3}\)và \(-2\sqrt{7}\)

Answer 1

* \(4\)và \(1+2\sqrt{2}\)

Ta có \(3=\sqrt{9}\)

           \(2\sqrt{2}=\sqrt{2^2.2}=\sqrt{8}\)

Ta lại có \(8< 9\Leftrightarrow\sqrt{8}< \sqrt{9}\)

Hay \(2\sqrt{2}< 3\)\(\Leftrightarrow1+2\sqrt{2}< 1+3\Leftrightarrow1+2\sqrt{2}< 4\)

Answer 2

* \(4\)và \(2\sqrt{6}-1\)

Ta có \(5=\sqrt{25}\)

          \(2\sqrt{6}=\sqrt{2^2.6}=\sqrt{24}\)

Ta lại có \(25>24\Leftrightarrow\sqrt{25}>\sqrt{24}\)

Hay \(5>2\sqrt{6}\Leftrightarrow5-1>2\sqrt{6}-1\Leftrightarrow4>2\sqrt{6}-1\)