Question

thực hiện phép tính

P=\(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)

Answer 1

\(P=\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)

\(=\dfrac{4\sqrt{2}-2\sqrt{3}}{3\sqrt{2}-4\sqrt{3}}-\dfrac{\left(\sqrt{5}+\sqrt{27}\right)\left(\sqrt{30}-\sqrt{162}\right)}{\left(\sqrt{30}+\sqrt{162}\right)\left(\sqrt{30}-\sqrt{162}\right)}\)

\(=\dfrac{\sqrt{6}\left(\dfrac{4\sqrt{3}}{3}-\sqrt{2}\right)}{3\left(\sqrt{2}-\dfrac{4\sqrt{3}}{3}\right)}-\dfrac{5\sqrt{6}-9\sqrt{10}+9\sqrt{10}-27\sqrt{6}}{30-162}\)

\(=\dfrac{-\sqrt{6}}{3}-\dfrac{-22\sqrt{6}}{-132}\)

\(=\dfrac{-\sqrt{6}}{3}-\dfrac{22\sqrt{6}}{132}\)

\(=\dfrac{-44\sqrt{6}}{132}-\dfrac{22\sqrt{6}}{132}=\dfrac{-66\sqrt{6}}{132}=\dfrac{-\sqrt{6}}{2}\)