\(A=\dfrac{8\sqrt{41}}{\sqrt{41}+2+\sqrt{41}-2}\cdot\dfrac{1}{\sqrt{3}-\sqrt{2}}\)

\(=\dfrac{4}{\sqrt{3}-\sqrt{2}}=4\sqrt{3}+4\sqrt{2}\)

a) Ta có: \(2\sqrt{8}-3\sqrt{18}+\sqrt{32}\)

\(=4\sqrt{2}-6\sqrt{2}+4\sqrt{2}\)

\(=2\sqrt{2}\)

b) Ta có: \(\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(1+\sqrt{2}\right)^2}\)

\(=\sqrt{2}-1+\sqrt{2}+1\)

\(=2\sqrt{2}\)

c) Ta có: \(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{4-2\sqrt{3}}\)

\(=2-\sqrt{3}+\sqrt{3}-1\)

=1

a: \(A=\sqrt{9-5-2\sqrt{3}}=\sqrt{4-2\sqrt{3}}=\sqrt{3}-1\)

b: Sửa đề: \(B=\sqrt{4+\sqrt{8}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}\)

\(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{4-2-\sqrt{2}}\)

\(=\sqrt{\left(4+2\sqrt{2}\right)\left(2-\sqrt{2}\right)}\)

\(=\sqrt{8-4\sqrt{2}+4\sqrt{2}-4}=2\)

\(C=\sqrt{x}+\frac{\sqrt[3]{2-\sqrt{3}}.\sqrt[6]{7+4\sqrt{3}}-x}{\sqrt[4]{9-4\sqrt{5}}.\sqrt{2+\sqrt{5}}+\sqrt{x}}\)

\(=\sqrt{x}+\frac{\sqrt[6]{\left(7-4\sqrt{3}\right).\left(7+4\sqrt{3}\right)}-x}{\sqrt[4]{\left(9+4\sqrt{5}\right).\left(9-4\sqrt{5}\right)}+\sqrt{x}}\)

\(=\sqrt{x}+\frac{1-x}{1+\sqrt{x}}=\sqrt{x}+\frac{\left(1+\sqrt{x}\right).\left(1-\sqrt{x}\right)}{1+\sqrt{x}}\)

\(=\sqrt{x}+1-\sqrt{x}=1\)

E = \(6x+\sqrt{9x^2-12x+4}\)

E = \(6x+\sqrt{\left(3x-2\right)^2}\)

E = \(6x+\left|3x-2\right|\)

E = \(6x+3x-2\)

E = \(9x-2\)

F = \(5x-\sqrt{x^2+4x+4}\)

F = \(5x-\sqrt{\left(x+2\right)^2}\)

F = \(5x-\left|x+2\right|\)

F = \(5x-x+2\)

F = \(4x+2\)