Cho mình sửa lại câu E nhé:

\(E=\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}-\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}=\dfrac{3-\sqrt{5}-3-\sqrt{5}}{\sqrt{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}}=\dfrac{-2\sqrt{5}}{2}=-\sqrt{5}\)

\(F=\left(\dfrac{1}{3-\sqrt{5}}-\dfrac{1}{3+\sqrt{5}}\right):\dfrac{5-\sqrt{5}}{\sqrt{5}-1}=\dfrac{3+\sqrt{5}-3+\sqrt{5}}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}.\dfrac{\sqrt{5}-1}{5-\sqrt{5}}=\dfrac{\sqrt{5}}{2}.\dfrac{1}{\sqrt{5}}=\dfrac{1}{2}\)

\(D=\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}\Rightarrow D< 0\)( do \(\sqrt{2-\sqrt{3}}< \sqrt{2+\sqrt{3}}\))\(\Rightarrow D^2=2-\sqrt{3}+2+\sqrt{3}-2\sqrt{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}=4-2=2\Rightarrow D=-\sqrt{2}\)

(do D<0)

\(E=\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}+\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}=\dfrac{3-\sqrt{5}+3+\sqrt{5}}{\sqrt{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}}=\dfrac{6}{2}=3\)

Bài 3: 

a) \(4^8.2^{20}=\left(2^2\right)^8.2^{20}=2^{36}\)

 \(9^{12}.27^5.81^4=\left(3^2\right)^{12}.\left(3^3\right)^5.\left(3^4\right)^4=3^{55}\)

\(64^3.4^5.16^2=\left(2^6\right)^3.\left(2^2\right)^5.\left(2^4\right)^2=2^{36}\)

b) \(25^{20}.125^4=5^{40}.5^{12}=5^{52}\)

\(x^7.x^4.x^3=x^{14}\)

\(3^6.4^6=\left(3.4\right)^6=12^6\)

c)\(8^4.2^3.16^2=2^{12}.2^3.2^8=2^{23}\)

\(2^3.2^2.8^3=2^3.2^2.2^9=2^{14}\)

\(y.y^7=y^8\)

By the time tommorow, the market will be being cleaned.

Mathematics is very interesting to me( D )

a) \(x^3+3x^2+3x=0\Rightarrow x\left(x^2+3x+3\right)=0\Rightarrow x\left[\left(x+\dfrac{3}{2}\right)^2+\dfrac{3}{4}\right]=0\Rightarrow x=0\)

(do \(\left(x+\dfrac{3}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}>0\))

b) \(x^3+6x^2+12x=0\Rightarrow x\left(x^2+6x+12\right)=0\Rightarrow x\left[\left(x+3\right)^2+4\right]=0\Rightarrow x=0\)

(do (x+3)²+4≥4>0)

\(\sqrt{x^2-6x+9}=4-x\left(đk:x\le4\right)\Leftrightarrow\sqrt{\left(x-3\right)^2}=4-x\Leftrightarrow\left|x-3\right|=4-x\Leftrightarrow\left[{}\begin{matrix}x-3=4-x\\3-x=4-x\left(loai\right)\end{matrix}\right.\Leftrightarrow x=\dfrac{7}{2}}\)

11) \(Na_2O+H_2O\rightarrow2NaOH\)

12) \(Ca\left(OH\right)_2+Na_2CO_3\rightarrow CaCO_3+2NaOH\)

13) \(Fe_2O_3+3H_2\rightarrow2Fe+3H_2O\)

14) \(Mg\left(OH\right)_2+2HCl\rightarrow MgCl_2+2H_2O\)

15) \(2FeI_3\rightarrow2FeI_2+I_2\)

16) \(3AgNO_3+K_3PO_4\rightarrow Ag_3PO_4+3KNO_3\)

17) \(SO_2+Ba\left(OH\right)_2\rightarrow BaSO_3+H_2O\)

18) \(2Ag+Cl_2\rightarrow2AgCl\)

19) \(FeS+2HCl\rightarrow FeCl_2+H_2S\)

20) \(Pb\left(OH\right)_2+2HNO_3\rightarrow Pb\left(NO_3\right)_2+2H_2O\)

1) \(MgCl_2+2KOH\rightarrow Mg\left(OH\right)_2+2KCl\)

2) \(Cu\left(OH\right)_2+2HCl\rightarrow CuCl_2+2H_2O\)

3) \(Cu\left(OH\right)_2+H_2SO_4\rightarrow CuSO_4+2H_2O\)

4) \(FeO+2HCl\rightarrow FeCl_2+H_2O\)

5) \(Fe_2O_3+3H_2SO_4\rightarrow Fe_2\left(SO_4\right)_3+3H_2O\)

6) \(Cu\left(NO_3\right)_2+2NaOH\rightarrow Cu\left(OH\right)_2+2NaNO_3\)

7) \(4P+5O_2\rightarrow2P_2O_5\)

8) \(N_2+O_2\rightarrow2NO\)

9) \(2NO+O_2\rightarrow2NO_2\)

10) \(4NO_2+O_2+2H_2O\rightarrow4HNO_3\)