Question

Rút gọn biểu thức: \(A=\dfrac{10.\sqrt{18}+5\sqrt{3}-15\sqrt{27}}{\sqrt{3}.\left(\sqrt{6}-4\right)}\)

Answer 1

\(A=\dfrac{10.\sqrt{18}+5\sqrt{3}-15\sqrt{27}}{\sqrt{3}.\left(\sqrt{6}-4\right)}\)

\(A=\dfrac{10.\sqrt{3.6}+5\sqrt{3}-15.\sqrt{3.3^2}}{\sqrt{3}.\left(\sqrt{6}-4\right)}\)

\(A=\dfrac{10.\sqrt{3}.\sqrt{6}+5\sqrt{3}-15.\sqrt{3}.3}{\sqrt{3}\left(\sqrt{6}-4\right)}\)

\(A=\dfrac{\sqrt{3}.\left(10.\sqrt{6}+5-15.3\right)}{\sqrt{3}\left(\sqrt{6}-4\right)}\)

\(A=\dfrac{10.\sqrt{6}+5-45}{\sqrt{6}-4}=\dfrac{10.\sqrt{6}-40}{\sqrt{6}-4}\)

\(A=\dfrac{10.\left(\sqrt{6}-4\right)}{\sqrt{6}-4}=10\)

Vậy \(A=10\)

Chúc bạn học tốt!!!