C = \(25.\left(-\frac{1}{3}\right)^3+\frac{1}{5}-2.\left(-\frac{1}{2}\right)^2-\frac{1}{2}\)

D = \(\left(-2\right)^3.\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\)

E = \(5\sqrt{16}-4\sqrt{9}+\sqrt{25}-0,3\sqrt{400}\)

F =\(\left(-\frac{3}{2}\right)+|-\frac{5}{6}|-1\frac{1}{2}:6\)

G = \(\frac{0,5+0,\left(3\right)-0,1\left(6\right)}{2,5+1,\left(6\right)-0,8\left(3\right)}\)

1. Tính giá trị biểu thức: \(A=\sqrt{a^2+4ab^2+4b}-\sqrt{4a^2-12ab^2+9b^4}\) với \(a=\sqrt{2}\) ; \(b=1\)

2. Đặt \(M=\sqrt{57+40\sqrt{2}}\) ; \(N=\sqrt{57-40\sqrt{2}}\). Tính giá trị của các biểu thức sau:

a) M-N

b) \(M^3-N^3\)

3. Chứng minh: \(\left(\frac{x\sqrt{x}+3\sqrt{3}}{x-\sqrt{3x}+3}-2\sqrt{x}\right)\left(\frac{\sqrt{x}+\sqrt{3}}{3-x}\right)=1\) (với \(x\ge0\) và \(x\ne3\))

4. Chứng minh: \(\frac{\left(\sqrt{a}-\sqrt{b}\right)^2+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}.\frac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}=a-b\) (a > 0 ; b > 0)

5. Chứng minh: \(\sqrt{9+4\sqrt{2}}=2\sqrt{2}+1\) ; \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}=5+3\sqrt{2}\) ; \(3-2\sqrt{2}=\left(1-\sqrt{2}\right)^2\)

6. Chứng minh: \(\left(\frac{1}{2\sqrt{2}-\sqrt{7}}-\left(3\sqrt{2}+\sqrt{17}\right)\right)^2=\left(\frac{1}{2\sqrt{2}-\sqrt{17}}-\left(2\sqrt{2}-\sqrt{17}\right)\right)^2\)

7. Chứng minh đẳng thức: \(\left(\frac{3\sqrt{2}-\sqrt{6}}{\sqrt{27}-3}-\frac{\sqrt{150}}{3}\right).\frac{1}{\sqrt{6}}=-\frac{4}{3}\)

8.Chứng minh: \(\frac{2002}{\sqrt{2003}}+\frac{2003}{\sqrt{2002}}>\sqrt{2002}+\sqrt{2003}\)

9. Chứng minh rằng: \(\sqrt{2000}-2\sqrt{2001}+\sqrt{2002}< 0\)

10. \(\frac{1}{2}+\frac{1}{3\sqrt{2}}+...+\frac{1}{\left(n+1\right)\sqrt{n}}< 2\) ; \(\frac{7}{5}< \frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}< \frac{29}{30}\)

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

2 Thực hiện phép tính

\(\frac{17}{9}-\frac{17}{9}:\left(\frac{7}{3}+\frac{1}{2}\right)\)

\(\frac{4}{3}.\frac{2}{5}-\frac{3}{4}.\frac{2}{5}\)

\(-\frac{3}{4}.5\frac{3}{13}-0.75.\frac{36}{13}\)

\(3.\left(-\frac{4}{3}\right)^2-\frac{7}{3}\)

\(-\frac{5}{7}.\frac{3}{11}+\frac{-5}{7}.\frac{8}{11}+3\frac{5}{7}\)

\(32\frac{1}{7}:\left(\frac{-5}{4}\right)-47\frac{1}{7}:\left(\frac{-5}{4}\right)\)

\(\left(\frac{2}{3}+\frac{1}{2}\right)^2-\frac{1}{12}\\ \frac{1}{4}-\frac{5}{12}:\frac{1}{6}+\frac{-6}{5}\\ \frac{17}{21}+\frac{5}{23}-\frac{1}{2}+\frac{4}{21}-1\frac{5}{23}\)

\(\left(-3\right)^2+\sqrt{\frac{16}{25}}-\sqrt{9}+\frac{\sqrt{81}}{3}\)

Thực hiện phép tính (Tính hợp lý nếu có thể)
g) \(\frac{3}{5}:\left(\frac{-1}{15}-\frac{1}{6}\right)+\frac{3}{5}:\left(\frac{-1}{3}-1\frac{1}{15}\right)\)

h) \(10.\sqrt{0,01}.\sqrt{\frac{16}{9}+3\sqrt{49}-\frac{1}{6}\sqrt{4}}\)

i) \(\frac{2^4.2^6}{\left(2^5\right)^2}-\frac{2^5.15^3}{6^3.10^2}\)

k) \((2\frac{1}{3}+3\frac{1}{2}):\left(-4\frac{1}{6}+3\frac{1}{7}\right)+7\frac{1}{2}\)

n) \(4\frac{25}{16}+25\left(\frac{9}{16}:\frac{125}{64}\right):\frac{-27}{8}\)

m) \([1,5+2\frac{1}{2}-\left(2\sqrt{2}\right)^2]:[4\frac{1}{2}-\sqrt{1,96}+0,9]\)

o) \(\frac{5}{21}.\left(4\frac{1}{5}.7\frac{3}{4}+5\frac{1}{4}.4,2\right)\)

p) \(\left(\frac{2}{5}+\frac{2}{7}-\frac{2}{11}\right):\left(\frac{3}{7}-\frac{3}{11}+\frac{3}{5}\right)\)

Làm nhanh làm đúng mình Tick nha :))