Question

thực hiện phép tính

Q=\(\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{\sqrt{2+1}}-\left(\sqrt{2}+\sqrt{3}\right)\)

Answer 1

\(Q=\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{\sqrt{2+1}}-\left(\sqrt{2}+\sqrt{3}\right)\)

\(=\dfrac{\left(3+2\sqrt{3}\right)\sqrt{3}}{3}+\dfrac{2+\sqrt{2}}{\sqrt{3}}-\sqrt{2}-\sqrt{3}\)

\(=\dfrac{3\sqrt{3}+6}{3}+\dfrac{\left(2+\sqrt{2}\right)\sqrt{3}}{3}-\sqrt{2}-\sqrt{3}\)

\(=\dfrac{3+\left(\sqrt{3}+2\right)}{3}+\dfrac{2\sqrt{3}+\sqrt{6}}{3}-\sqrt{2}-\sqrt{3}\)

\(=\sqrt{3}+2+\dfrac{2\sqrt{3}+\sqrt{6}}{3}-\sqrt{2}-\sqrt{3}\)

\(=2+\dfrac{2\sqrt{3}+\sqrt{6}}{3}-\sqrt{2}\)