Rút Gọn :

A=\(\dfrac{x-3}{\sqrt{x-1}-\sqrt{2}}\)

Tìm giá trị lớn nhất của hàm số

y=\(\dfrac{x^2+2x+8}{x^2+2x+3}\)

\(\sqrt{3+\sqrt{5+2\sqrt{3}}}.\sqrt{3-\sqrt{5+2\sqrt{3}}}\)

\(\sqrt{\dfrac{3}{4}}\) +\(\sqrt{\dfrac{1}{3}}\) +\(\sqrt{\dfrac{1}{12}}\)

\(\sqrt{7+4\sqrt{3}}.\sqrt{7-4\sqrt{3}}\)

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

Rút gọn:

a.\(\sqrt{3a}.\sqrt{27a}-5a\left(a\ge0\right)\)

b.\(\left(2-a\right)^2-\sqrt{0,3}.\sqrt{30a^2}\)

\(\sqrt{2}.\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4}+\sqrt{15}\)

Giải phương trình

\(\left(x^2+x+2\right)^2-\left(x+1\right)^3=x^6+1\)

Thực hiện phép tính:

\(1,\left(\sqrt{12}-2\sqrt{75}\right).\sqrt{3}\)

\(2,\sqrt{3}.\left(\sqrt{12}.\sqrt{27}-\sqrt{3}\right)\)

\(3,\left(7\sqrt{48}+3\sqrt{27}-2\sqrt{12}\right):\sqrt{3}\)

\(4,\left(\sqrt{\dfrac{1}{7}}-\sqrt{\dfrac{16}{7}}+\sqrt{7}\right):\sqrt{7}\)

\(5,\sqrt{\sqrt{5}+2}.\sqrt{\sqrt{5}-2}\)

\(6,\sqrt{9-\sqrt{17}}.\sqrt{9+\sqrt{17}}\)