Rút gọn

a) \(\sqrt{8+4\sqrt{3}}\)

b) \(\sqrt{2}.\sqrt{4+\sqrt{15}}\)

c) \(\sqrt{2x-2\sqrt{x^2-4}}\) với a≥2

Tìm gtnn của

A= \(\sqrt{x^2-5x+10}\)

B= \(\sqrt{2x^2-x-7}\)

C= \(x^2+2y^2+2xy-2x+y\)

Rút gọn

A= \(\sqrt{13+4\sqrt{10}-\sqrt{13-4\sqrt{10}}}\)

B= \(\sqrt{\dfrac{3-2\sqrt{2}}{17-12\sqrt{2}}+\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}}\)

C= \(\dfrac{\sqrt{x^2+9x+6}}{x+3}\)

D= \(\sqrt{2m+4+6\sqrt{2m-5}}-\sqrt{2m-5}\)

tìm đkxđ:

a) \(\dfrac{1}{\sqrt{x-1}}\)

b) \(\dfrac{1}{\sqrt{x-\sqrt{2x-1}}}\)

c) \(\sqrt{-\dfrac{1}{x}}\)

d) \(\sqrt{\dfrac{a+1}{a^2}}\)

CM: a\(^4\)+b\(^4\)+c\(^4\)-1 ≥ 2a(ab\(^2\)+c-a+1)