Question

[Siêu Văn Nhân]

Bài : Tính

(\(\sqrt{6}+\sqrt{2}\) ).\(\sqrt{2-\sqrt{3}}\)

Bài 2 : Rút gọn

a,B= \(\sqrt{\dfrac{3\sqrt{5}+1}{2\sqrt{5}-3}}.\left(\sqrt{10}-\sqrt{2}\right)\)

b, C= \(\left(\sqrt{7+4\sqrt{3}}\right)^3.\left(2-\sqrt{3}\right)^3\)

c, A= \(\sqrt{24-16\sqrt{2}}+\sqrt{12-8\sqrt{2}}\)

d, Q= \(\dfrac{x\sqrt{x}-2x-4\sqrt{x}+6}{x-3\sqrt{x}+2}-\dfrac{\sqrt{x}-2}{\sqrt{x}-1}-\dfrac{\sqrt{x}}{2-\sqrt{x}}\)

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Answer 1

[Lam Tinh Tuyết]

\(b1:=\sqrt{2}\left(\sqrt{3}+1\right).\sqrt{2-\sqrt{3}}\\ =\left(\sqrt{3}+1\right).\sqrt{4-2\sqrt{3}}\\ =\left(\sqrt{3}+1\right).\left(\sqrt{3}-1\right)\\ =2\\ \\ b2:a,=\sqrt{\dfrac{\left(3\sqrt{5}+1\right)\left(2\sqrt{5}-3\right)}{\left(2\sqrt{5}-3\right)^2}}.\left(\sqrt{10}-\sqrt{2}\right)\\ =\dfrac{\sqrt{27-7\sqrt{5}}}{2\sqrt{5}-3}.\left(\sqrt{10}-\sqrt{2}\right)\\ =\dfrac{\sqrt{2}}{\sqrt{2}}.\dfrac{\sqrt{27-7\sqrt{5}}}{2\sqrt{5}-3}.\left(\sqrt{10}-\sqrt{2}\right)\\ =\dfrac{\sqrt{54-14\sqrt{5}}}{2\sqrt{10}-3\sqrt{2}} .\left(\sqrt{10}-\sqrt{2}\right)\\ \)\(=\dfrac{\sqrt{\left(7-\sqrt{5}\right)^2}}{2\sqrt{10}-3\sqrt{2}}.\left(\sqrt{10}-\sqrt{2}\right)\)\(\\ =\dfrac{8\sqrt{10}-12\sqrt{2}}{2\sqrt{10}-3\sqrt{2}}\\ =4\)