Question

Không dùng máy tính, hãy so sánh:

A=\(2+\sqrt{3}\)   

B= \(\sqrt{2}\)+3

 

 

Answer 1

\(A^2=\left(2+\sqrt{3}\right)^2=7+\sqrt{48}\)

\(B^2=\left(\sqrt{2}+3\right)^2=11+\sqrt{72}\)

\(\hept{\begin{cases}7< 11\\\sqrt{48}< \sqrt{72}\end{cases}\Leftrightarrow}7+\sqrt{48}< 11+\sqrt{72}\)

\(\Rightarrow A< B\)

Answer 2

Ta có:\(2+\sqrt{3}< 2+\sqrt{4}=4=\sqrt{1}+3< \sqrt{2}+3\)

   \(\Rightarrow2+\sqrt{3}< \sqrt{2}+3\)