Question

[Nguyễn Thùy Linh]

So sánh :

a) \(2\sqrt{3}\)và \(3\sqrt{2}\)

b) \(4\sqrt{3}\)và \(3\sqrt{4}\)

Answer 1

[Nhật Hạ]

Cách 1:

a, Ta  có: \(2\sqrt{3}=\sqrt{4.3}=\sqrt{12}\); \(3\sqrt{2}=\sqrt{9.2}=\sqrt{18}\)

Vì 18 > 12 \(\Rightarrow\sqrt{18}>\sqrt{12}\)\(\Rightarrow3\sqrt{2}>2\sqrt{3}\)

b, Ta có: \(4\sqrt{3}=\sqrt{16.3}=\sqrt{48}\); \(3\sqrt{4}=\sqrt{9.4}=\sqrt{36}\)

Vì 48 > 36 \(\Rightarrow\sqrt{48}>\sqrt{36}\)\(\Rightarrow4\sqrt{3}>3\sqrt{4}\)

Cách 2:

Đặt \(A=2\sqrt{3}\)\(\Rightarrow A^2=\left(2\sqrt{3}\right)^2=4.3=12\)

      \(B=3\sqrt{2}\)\(\Rightarrow B^2=\left(3\sqrt{2}\right)^2=9.2=18\)

Vì 12 < 18 => A² < B² => A < B 

b, Đặt \(A=4\sqrt{3}\)\(\Rightarrow A^2=\left(4\sqrt{3}\right)^2=16.3=48\)

\(B=3\sqrt{4}\)\(\Rightarrow B^2=\left(3\sqrt{4}\right)^2=9.4=36\)

Vì 48 > 36 => A² > B² => A > B

Answer 2

[Nguyễn Xuân Thành đoàn]

Bình Tất cả lên

a)  2sqrt(3) < 3sqrt(2)