Rút gọn :
a) \(\sqrt{4+2\sqrt{3}}-\sqrt{5+2\sqrt{6}}+\sqrt{2}\)
b) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
Rút gọn:
a) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+\sqrt{48}}}}\)
b) \(\dfrac{\sqrt{3}-\sqrt{5+\sqrt{24}}+\sqrt{\sqrt{72}+11}}{\sqrt{6+\sqrt{20}}+\sqrt{2}-\sqrt{7+\sqrt{40}}}\)
Tìm điều kiện xác định và rút gọn A
\(A=\left(\dfrac{4x\sqrt{x}+3x+9}{x+5\sqrt{x}+6}-\dfrac{3-\sqrt{x}}{2+\sqrt{x}}\right)\div\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}-\dfrac{3+4\sqrt{x}}{x+5\sqrt{x}+6}\right)\)
Tính:
\(A=\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+\dfrac{1}{4\sqrt{3}+3\sqrt{4}}+...+\dfrac{1}{225\sqrt{224}+224\sqrt{225}}\)
a) Tính \(M=\sqrt{a^2+4ab^2+4b^4}-\sqrt{4a^2-12ab^2+9b^4}\)
Với \(a=\sqrt{2};b=1\)
b) Tính \(\dfrac{\sqrt{x}+\sqrt{3}}{3-x}.\left(\dfrac{x\sqrt{x}+3\sqrt{3}}{x-\sqrt{3x}+3}-2\sqrt{x}\right)\)
\(A=\left(\dfrac{\sqrt{x}+2}{x-5\sqrt{x}+6}-\dfrac{\sqrt{x}+3}{2-\sqrt{x}}-\dfrac{\sqrt{x}+2}{\sqrt{x}-3}\right):\left(2-\dfrac{\sqrt{x}}{\sqrt{x}+1}\right)\)
a) Rút gọn A
b) Cho |x| = 3. Tính A
Rút gọn \(A=\left(\dfrac{6x+4}{3\sqrt{3x^3}-8}-\dfrac{\sqrt{3x}}{3x+2\sqrt{3x}+4}\right).\left(\dfrac{1+3\sqrt{3x^3}}{1+\sqrt{3x}}-\sqrt{3x}\right)\)
\(\frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+.......+\frac{1}{1001\sqrt{1000}}+\frac{1}{1002\sqrt{1001}}< \sqrt{2}\)
tính gt bt
a/\(P=\sqrt{1^3+\dfrac{1^2}{3}}+\sqrt{2^3+\dfrac{3^2}{5}}+\sqrt{3^3+\dfrac{5^2}{7}}+...+\sqrt{75^3+\dfrac{149^2}{151}}\)
