Thực hiện phép tính.

1) \(\sqrt[3]{\sqrt{2}+1}.\sqrt[3]{3+2\sqrt{2}}:\sqrt[3]{\left(4-2\sqrt{3}\right)\left(\sqrt{3}-1\right)}\)

2)  \(\left(\frac{1}{2}.\sqrt[3]{9}-2.\sqrt[3]{3}+3.\sqrt[3]{\frac{1}{3}}\right):2.\sqrt[3]{\frac{1}{3}}\)

3)  \(\left(\sqrt[3]{4}+1\right)^3-\left(\sqrt[3]{4}-1\right)^3\)

4)  \(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\frac{1}{4}\sqrt{8}\right).3\sqrt{6}\)

Thực hiện phép tính

1)\(\frac{\sqrt{4+\sqrt{7}}+\sqrt{4-\sqrt{7}}+\sqrt{2}}{\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}+\sqrt{5}}\)

2)\(\left(4+\sqrt{15}\right)\left(10-\sqrt{6}\right)-\sqrt{4-\sqrt{15}}\)

3)\(\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)

4)\(\frac{2\sqrt{3-\sqrt{5+\sqrt{13-\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)

5)\(\frac{1+\frac{\sqrt{3}}{2}}{1+\sqrt{1+\frac{\sqrt{3}}{2}}}+\frac{1-\frac{\sqrt{3}}{2}}{1-\sqrt{1-\frac{\sqrt{3}}{2}}}\)

Bài 2: Thực hiện phép tính

a) \(\sqrt{5}-\sqrt{48}+5\sqrt{27}-\sqrt{45}\)

b) \(\left(\sqrt{5}+\sqrt{2}\right)\left(3\sqrt{2}-1\right)\)

c) \(3\sqrt{50}-2\sqrt{75}-4\frac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\frac{1}{3}}\)

d) \(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4-2\sqrt{3}}\)

e) \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)

f) \(\frac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\frac{6}{2-\sqrt{10}}-\frac{20}{\sqrt{10}}\)

Bài 3: Thực hiện phép tính

a) \(\sqrt{9-4\sqrt{5}}\)

b) \(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)

c) \(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)

d) \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)

e) \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)

f*) \(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)

Bài 4: Rút gọn

a) \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}\)

b) \(\left(2\sqrt{3}+\sqrt{4}\right)\left(\sqrt{3}-2\right)\)

c) \(\sqrt{3+2\sqrt{2}}+\sqrt{\left(\sqrt{2}-2\right)^2}\)

d) \(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}+\sqrt{6}\)

e) \(\left(\frac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\frac{4}{1+\sqrt{5}}+4\right)\)

f) \(\frac{1}{5}\sqrt{50}-2\sqrt{96}-\frac{\sqrt{30}}{\sqrt{15}}+12\sqrt{\frac{1}{6}}\)

thực hiện phép tính: a)\(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}+\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)

b)\(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}+\frac{\sqrt{5}+1}{\sqrt{5}-1}\)

c)\(2\sqrt{18\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{5\sqrt{48}}\)

d)\(\left(2\sqrt{5}+\sqrt{12}\right)\left(\sqrt{3}-\sqrt{5}\right)\)

e)\(\sqrt{2}+\sqrt{\frac{1}{2}}+\sqrt{72}-\sqrt{\frac{3}{2}}\)

f)\(\sqrt{2}\sqrt{2+\sqrt{3}}-2\left(\sqrt{3}-1\right)\)

g)\(\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}-\left(2\sqrt{3}-2007\right)\)

Rút gọn biểu thức:

\(A=\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\frac{1}{\sqrt{4}-\sqrt{5}}\)

\(B=\left(\frac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\frac{4}{1+\sqrt{5}}+4\right)\)

\(C=\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right):\left(1:\frac{1}{\sqrt{2}+\sqrt{3}}\right)\)

\(D=2\sqrt{50}-\frac{1}{\sqrt{2}-1}+4\sqrt{\frac{9}{2}}-\sqrt{3-2\sqrt{2}}\)

Bài 7 Thực hiện phép tính 

a ( \(\frac{\sqrt{9}}{2}+\frac{\sqrt{1}}{2}-\sqrt{2}\)  ) \(\sqrt{2}\)

b) \(\left(\frac{\sqrt{8}}{3}-\sqrt{24}+\frac{\sqrt{50}}{3}\right)\sqrt{6}\)

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

d) \(\left(3\sqrt{2}+1\right)\left(3\sqrt{2}-1\right)\)

e ) (\(\left(\sqrt{5}-2\sqrt{3}\right)\left(\sqrt{5}+2\sqrt{3}\right)\)

g)\(\left(\frac{\sqrt{2}}{3}-\sqrt{\frac{3}{2}}\right)^2\)

h) \(\sqrt{52}:\sqrt{117}\)

i) \(\sqrt{2}:\sqrt{72}\)

l ) \(\left(\frac{\sqrt{1}}{5}-\frac{\sqrt{9}}{5}\right)+\sqrt{5}\)

k) \(\left(\sqrt{12}+\sqrt{27}-\sqrt{3}\right):\sqrt{3}\)

m) \(\frac{\sqrt{2}+\sqrt{3}}{\sqrt{3}}\)

n) \(\frac{\sqrt{6-2\sqrt{5}}}{1-\sqrt{5}}\)