Xét VT :\(\left(4-\sqrt{7}\right)^2=14-8\sqrt{7}+7=23-8\sqrt{7}\)

=> VT=VP ( đpcm)

\(\left(4-\sqrt{7}\right)^2=4^2-2\cdot4\cdot\sqrt{7}+7=23-8\sqrt{7}\)

a) \(9+4\sqrt{5}=4+4\sqrt{5}+5=2^2+2\cdot2\sqrt{5}+\left(\sqrt{5}\right)^2=\left(\sqrt{5}+2\right)^2\left(ĐPCM\right)\)

a) \(9+4\sqrt{5}=\left(\sqrt{5}\right)^2+2.\sqrt{5}.2+2^2=\left(\sqrt{5}+2\right)^2\left(đpcm\right)\)

b)\(\sqrt{9-4\sqrt{5}}-\sqrt{5}=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}=\sqrt{5}-2-\sqrt{5}=-2\left(đpcm\right)\)

c)\(\left(4-\sqrt{7}\right)^2=16-8\sqrt{7}+7=23-8\sqrt{7}\left(đpcm\right)\)

d)\(\sqrt{23+8\sqrt{7}}-\sqrt{7}=\sqrt{\left(4+\sqrt{7}\right)^2}-\sqrt{7}=4+\sqrt{7}-\sqrt{7}=4\left(đpcm\right)\)

a) \(\left(\sqrt{5}+2\right)^2=\sqrt{5}^2+4\sqrt{5}+4=5+4\sqrt{5}+4=9+4\sqrt{5}\left(dpcm\right)\)

cậu ơi làm câu 2 lun đi 

\(\left(4-\sqrt{7}\right)^2=4^2-2\cdot4\cdot\sqrt{7}+7\)

\(=16-8\sqrt{7}+7=23-8\sqrt{7}\)

\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)

\(=\sqrt{5-2\cdot\sqrt{5}\cdot2+4}-\sqrt{5}\)

\(=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{5}\)

\(=\left|\sqrt{5}-2\right|-\sqrt{5}\)

\(=\sqrt{5}-2-\sqrt{5}=-2\)

\(\dfrac{\sqrt{4-2\sqrt{3}}}{1+\sqrt{2}}:\dfrac{\sqrt{2}-1}{\sqrt{3}+1}\)

\(=\dfrac{\sqrt{3-2\cdot\sqrt{3}\cdot1+1}}{\sqrt{2}+1}\cdot\dfrac{\sqrt{3}+1}{\sqrt{2}-1}\)

\(=\dfrac{\sqrt{\left(\sqrt{3}-1\right)^2}}{\sqrt{2}+1}\cdot\dfrac{\sqrt{3}+1}{\sqrt{2}-1}\)

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

\(\left(\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\dfrac{\sqrt{216}}{3}\right)\cdot\dfrac{1}{\sqrt{6}}\)

\(=\left(\dfrac{\sqrt{6}\left(\sqrt{2}-1\right)}{2\left(\sqrt{2}-1\right)}-\dfrac{6\sqrt{6}}{3}\right)\cdot\dfrac{1}{\sqrt{6}}\)

\(=\left(\dfrac{1}{2}\sqrt{6}-2\sqrt{6}\right)\cdot\dfrac{1}{\sqrt{6}}\)

\(=\dfrac{1}{2}-2=-\dfrac{3}{2}=-1,5\)

a. 9+4\(\sqrt{5}\)=(\(\sqrt{5}\)​+2)2

VT: 9+4\(\sqrt{5}\)=2\(^2\)+2.2.​\(\sqrt{5}\)​+​​(\(\sqrt{5}\))\(^2\)=(2+\(\sqrt{5}\))\(^2\)=VP

b. \(\sqrt{23+8\sqrt{7}}\)-\(\sqrt{7}\)=4

\(\Leftrightarrow\)\(\sqrt{4^2+2.4\sqrt{7}+\left(\sqrt{7}\right)^2}\)-\(\sqrt{7}\)=4

\(\Leftrightarrow\)\(\sqrt{4+\sqrt{7}}^2\)-\(\sqrt{7}\)=4

\(\Leftrightarrow\)4+\(\sqrt{7}\)-\(\sqrt{7}\)=4

\(\Leftrightarrow\)4=4

\(\Rightarrow\)VT=VP
\(\sqrt{5}\)\(\sqrt{5}\)

Ta có \(7^4\) chia hết cho 7; \(7^8\) chia hết cho 7; ... \(7^{36}\) chia hết cho 7

\(\Rightarrow7^4+7^8+...+7^{36}\) chia hết cho 7

Mà 1 không chia hết cho 7

\(\Rightarrow E=1+7^4+7^8+...+7^{36}\) không chia hết cho 7

Mà 35 chia hết cho 7

\(\Rightarrow E\) không chia hết cho 35

\(\Rightarrow\) Đề sai for sure!