Bài 1: Thực hiện phép tính:

a,\(\left(\frac{-3}{4}+\frac{2}{7}\right):\frac{2}{7}+\left(\frac{-1}{4}+\frac{5}{7}\right):\frac{2}{3}\)

b,\(\left(-\frac{1}{3}\right)^2\cdot\frac{4}{11}+\frac{7}{11}\cdot\left(-\frac{1}{3}\right)^2\)

c, \(\left(-\frac{1}{7}\right)^0-2\frac{4}{9}\cdot\left(\frac{2}{3}\right)^2\)

d,\(\frac{2^7\cdot9^2}{3^3\cdot2^5}\)

e,\(\left(\frac{1}{3}-\frac{5}{6}\right)^2+\frac{5}{6}:2\)

f,\(\left(9\frac{2}{4}:5,2+3.4\cdot2\frac{7}{34}\right):\left(-1\frac{9}{16}\right)\)

g,\(\sqrt{25}-3\sqrt{\frac{4}{9}}\)

h,\(\left(-2\right)^2+\sqrt{36}-\sqrt{9}+\sqrt{25}\)

i,\(\left(-\frac{1}{2}\right)^4+\left|-\frac{2}{3}\right|-2007^0\)

k,\(\left(-2\right)^3+\frac{1}{2}:\frac{1}{8}-\sqrt{25}+\left|-64\right|\)

m,\(\left(-3\right)^2\cdot\frac{1}{3}-\sqrt{49}+\left(-5\right)^3:\sqrt{25}\)

n,\(\frac{\sqrt{3^2+\sqrt{39^2}}}{\sqrt{91^2}-\sqrt{\left(-7\right)^2}}\)

1) Rút gọn biểu thức theo là cách hợp lý:

A = \(\frac{1-\frac{1}{\sqrt{49}}+\frac{1}{49}-\frac{1}{\left(7\sqrt{7}\right)^2}}{\frac{\sqrt{64}}{2}-\frac{4}{7}+\left(\frac{2}{7}\right)^2-\frac{4}{343}}\)

2) Tính hợp lý:

M = \(1-\frac{5}{\sqrt{196}}-\frac{5}{\left(2\sqrt{21}\right)^2}-\frac{\sqrt{25}}{204}-\frac{\left(\sqrt{5}\right)^2}{374}\)

3) Có hay không giá trị của x thỏa mãn điều kiện sau:

\(2002.\sqrt{\left(1+x\right)^2}+2003.\sqrt{\left(1-x\right)^2}=0\)

4) Tìm các số x, y, z thỏa mãn đẳng thức:

\(\sqrt{\left(x-\sqrt{2}\right)^2}+\sqrt{\left(y+\sqrt{2}\right)^2}+\left|x+y+z\right|=0\)

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)\(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}+2\right)\left(\frac{\sqrt{2}+\sqrt{3}}{4\sqrt{2}}-\frac{\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right)\left(24+8\sqrt{6}\right)\left(\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{2}-\sqrt{3}}\right)\)

Bài 2. Tính giá trị biểu thức

a/ \(2\sqrt{27}-\sqrt{\frac{16}{3}}-\sqrt{48}-\sqrt{8\frac{1}{3}}\)

b/ \(\left(3\sqrt{20}-\sqrt{125}-15\sqrt{\frac{1}{5}}\right)\sqrt{5}\)

c/\(\left(2\sqrt{48}-\frac{3}{2}\sqrt{\frac{4}{3}}+\sqrt{27}\right).2\sqrt{3}\)

d/ \(\sqrt{\left(3-2\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{8}-4\right)^2}\)

e/ \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{\left(3-\sqrt{15}\right)^2}\)