tính

1.\(\left(\sqrt{15}-2\sqrt{3}\right)^2+12\sqrt{5}\)

2.\(3\sqrt{2}\left(4-\sqrt{2}\right)+3\left(1-2\sqrt{2}\right)^2\)

3.\(\dfrac{1}{2}\left(\sqrt{6}+\sqrt{5}\right)^2-\dfrac{1}{4}\sqrt{120}-\sqrt{\dfrac{15}{2}}\)

4.\(\left(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\right)^2\)

5.\(\left(\sqrt{\sqrt{14}+\sqrt{5}}+\sqrt{\sqrt{14}-\sqrt{5}}\right)^2\)

6.\(\left(\sqrt{3}+1\right)^3-\left(\sqrt{3}-1\right)^3\)

7.\(\left(\sqrt{2}+1\right)^3-\left(\sqrt{2}-1\right)^3\)

8.\(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)

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

1, \(\sqrt{\left(2+\sqrt{5}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)}^2\)

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

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

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

5, \(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)

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

Tính:
\(A=2\sqrt{\left(-3\right)^6}+2\sqrt{\left(-2\right)^4}-4\sqrt{\left(-2\right)^6}\)

\(B=\sqrt{\left(\sqrt{2}-2\right)^2}+\sqrt{\left(\sqrt{2}-3\right)^2}\)
\(C=\sqrt{\left(3-\sqrt{3}\right)^2}-\sqrt{\left(1+\sqrt{3}\right)^2}\)
\(D=\sqrt{\left(5+\sqrt{6}\right)^2}-\sqrt{\left(\sqrt{6}-5\right)^2}\)
\(E=\sqrt{17^2-8^2}-\sqrt{3^2+4^2}\)

Thực hiện phép tính

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

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

c)\(4.\sqrt{\left(2-\dfrac{\sqrt{3}}{2}\right)^2}-3.\sqrt{\left(\sqrt{3}-1\right)^2}\)

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

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

g)\(\left(1-2\sqrt{2}\right)^2-\left(\sqrt{2}+1\right)^2\)

Rút gọn :

\(\dfrac{\sqrt{x+\sqrt{4\left(x-1\right)}}-\sqrt{x-\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(\sqrt{x-1}-\dfrac{1}{\sqrt{x-1}}\right)\)

b)\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)

c)\(\left(\sqrt{5}+1\right)\left(\sqrt{7}+1\right)\left(\sqrt{35}+1\right)\left(34-4\sqrt{7}-6\sqrt{5}\right)\)

d) \(\left(\sqrt{7}+1\right)\left(2\sqrt{2}-1\right)\left(2\sqrt{14}-1\right)\left(55+12\sqrt{2}-7\sqrt{7}\right)\)

e)\(\left(3\sqrt{2}+1\right)\left(2\sqrt{3}+1\right)\left(6\sqrt{6}+1\right)\left(215-34\sqrt{3}-33\sqrt{2}\right)\)

Rút gọn biểu thức 
1) \(\frac{\sqrt{5+2\sqrt{6}}+\sqrt{8+2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
2) \(\left(2+\frac{3+\sqrt{3}}{\sqrt{3}+1}\right)\left(2+\frac{3-\sqrt{3}}{\sqrt{3}-1}\right):\left(\sqrt{5}-2\right)\)
3) \(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right).\left(\sqrt{6}+11\right)\)
4) \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\)
5) \(\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-...-\frac{1}{\sqrt{98}-\sqrt{99}}+\frac{1}{\sqrt{99}-\sqrt{100}}\)
6) \(\frac{1}{2+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{100\sqrt{99}+99\sqrt{100}}\)
7)\(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}+2\right)\left(\frac{\sqrt{2}+\sqrt{3}}{4\sqrt{2}}-\frac{\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right)\left(24+8\sqrt{6}\right)\left(\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{2}-\sqrt{3}}\right)\)

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