Question

Thực hiện phép tính:

a) \(\sqrt{48-2\sqrt{ }135}-\sqrt{45}+\sqrt{18}\)

b) \(\dfrac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\dfrac{6}{2-\sqrt{10}}-\dfrac{20}{\sqrt{10}}\)

Answer 1

\(A=\sqrt{45-2\sqrt{135}+3}-3\sqrt{5}+3\sqrt{2}\\ =\sqrt{\left(3\sqrt{5}-\sqrt{3}\right)^2}-3\sqrt{5}+3\sqrt{2}\\ =3\sqrt{5}-\sqrt{3}-3\sqrt{5}+3\sqrt{2}\\ =3\sqrt{2}-\sqrt{3}\)

Answer 2

\(B=\dfrac{\sqrt{5}.\sqrt{2}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{5}-\sqrt{2}}-\dfrac{6\left(2+\sqrt{10}\right)}{10-4}-2\sqrt{10}\\ =\sqrt{10}-\dfrac{12+6\sqrt{10}}{6}-2\sqrt{10}\\ =\sqrt{10}-2-\sqrt{10}-2\sqrt{10}\\ =-2-2\sqrt{10}\)