Question

So sánh: \(2\sqrt{3}\) và \(3\sqrt{2}\)

Answer 1

Đặt A = \(2\sqrt{3}\), B = \(3\sqrt{2}\). Ta có:

A = \(2\sqrt{3}\)

\(\Rightarrow\) A² = (\(2\sqrt{3}\))² = 4 . 3 = 12

B = \(3\sqrt{2}\)

\(\Rightarrow\) B² = (\(3\sqrt{2}\))² = 9 . 2 = 18

VÌ 18 > 12 nên A < B hay \(2\sqrt{3}\) < \(3\sqrt{2}\)

Vậy...

Answer 2

Ta có \(2\sqrt{3}=\sqrt{2^2.3}=\sqrt{4.3}=\sqrt{12}\)

\(3\sqrt{2}=\sqrt{3^2.2}=\sqrt{9.2}=\sqrt{18}\)

Vì \(18>12\Leftrightarrow\sqrt{18}>\sqrt{12}\Leftrightarrow3\sqrt{2}>2\sqrt{3}\)

Vậy \(2\sqrt{3}< 3\sqrt{2}\)