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

=>\(\sqrt{9-4\sqrt{5}}=\left(2-\sqrt{5}\right)\)=> điều cần phải chứng minh 

Câu a thì c/m được câu b đề yêu cầu gì thế.

a) Xét VP được :

\(\left(\sqrt{5}+2\right)^2\) sử dụng hàng đẳng thức số 1 :

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

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

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

Ta biến đổi vế phải :

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

=> Ta có VT= VP <=> VP = VT

b) Thiếu đề =.= sao làm

b,

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

\(=\sqrt{4-2.2\sqrt{5}+5}-\sqrt{5}\)

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

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

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

mấy bác tranh câu a e làm câu b

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Sửa đề: \(\sqrt{9-4\sqrt{5}}-\sqrt{5}\left(1-\sqrt{5}\right)\)

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

=3