\(\sqrt{36-12\sqrt{5}}\)

\(=\sqrt{9-2\cdot3\cdot2\sqrt{5}+20+7}\)

\(=\sqrt{3^2-2\cdot3\cdot2\sqrt{5}+\left(2\sqrt{5}\right)^2+7}\)

\(=\sqrt{\left(3-2\sqrt{5}\right)^2+7}\)

\(\sqrt{29+12\sqrt{5}}\)

= \(\sqrt{\left(2\sqrt{5}\right)^2+2.3.2\sqrt{5}+9}\)

= \(2\sqrt{5}+3\)

\(\sqrt{29+12\sqrt{5}}\)

\(=\sqrt{9+2\cdot3\cdot2\sqrt{5}+20}\)

\(=\sqrt{3^2+2\cdot3\cdot2\sqrt{5}+\left(2\sqrt{5}\right)^2}\)

\(=\sqrt{\left(3+2\sqrt{5}\right)^2}\)

\(=\left|3+2\sqrt{5}\right|=3+2\sqrt{5}\)

\(B=x+\sqrt{x}=\sqrt{x}\left(\sqrt{x}+1\right).\)

Vì \(\sqrt{x}\ge0\)\(\Rightarrow B_{min}\)\(=0\Leftrightarrow\sqrt{x}\left(\sqrt{x}+1\right)=0\)

\(\Rightarrow\hept{\begin{cases}\sqrt{x}=0\\\sqrt{x}+1=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\x\in\varnothing\end{cases}}}\)

Vậy \(B_{min}=0\Leftrightarrow x=0\)

\(B=x+\sqrt{x}\)

\(B=\left(\sqrt{x}\right)^2+2\cdot\frac{1}{2}\sqrt{x}+\left(\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^2\)

\(B=\left(\sqrt{x}+\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^2\)

\(B=\left(\sqrt{x}+\frac{1}{2}\right)^2-\frac{1}{4}\)

Có \(\left(\sqrt{x}+\frac{1}{2}\right)^2\ge0\)

\(\Rightarrow\left(\sqrt{x}+\frac{1}{2}\right)^2-\frac{1}{4}\ge-\frac{1}{4}\)

\(\Rightarrow GTNN\left(\sqrt{x}+\frac{1}{2}\right)^2-\frac{1}{4}=-\frac{1}{4}\)

\(\Rightarrow GTNNx+\sqrt{x}=-\frac{1}{4}\)

với \(\left(\sqrt{x}+\frac{1}{2}\right)^2=0\)

Đkxđ:\(x\ge0\)

TA có: \(B=x+\sqrt{x}\Rightarrow B=\sqrt{x}\left(\sqrt{x}+1\right)\ge0\) 

Dấu "=" xảy ra <=> \(\orbr{\begin{cases}\sqrt{x=0}\Leftrightarrow x=0\\\sqrt{x}+1=0\Leftrightarrow\sqrt{x}=-1\left(ktm\right)\end{cases}}\) 

Vậy min B=0 tại x=0

\(\left(\frac{15}{3-\sqrt{3}}-\frac{2}{1-\sqrt{3}}+\frac{3}{\sqrt{3}-2}\right):\sqrt{28+10\sqrt{3}}\)

\(=\left(\frac{15}{3-\sqrt{3}}-\frac{2}{1-\sqrt{3}}+\frac{3}{\sqrt{3}-2}\right):\sqrt{3}+5\)

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

\(=-\frac{5\sqrt{3}-8}{5-3\sqrt{3}}:\sqrt{3}+5\)

\(=-\frac{5\sqrt{3}-8}{\left(5-3\sqrt{3}\right)\left(5+3\sqrt{3}\right)}\)

\(=-\frac{5\sqrt{3}-8}{16-10\sqrt{3}}\)

= -(-1/2) = 1/2

49 + 20 căn 6 =  25 + 2.5.(2 căn 6) +24 =  (5 + 2 căn 6)²

tương tự vs 49 - 20 căn 6 = (5 - 2 căn 6)² =) căn ( 49 - 20 căn 6 ) = 5 - 2 căn 6

7 - 4 căn 3 = 4 - 4 căn 3 + 3 = (2 - căn 3)²  =) căn ( 7 - 4 căn 3 ) = 2 - căn 3

tự giải nhé

gợi ý nhé

5 + 2 căn 6 = 2 + 2 căn 6 + 3 ( để ý thấy 6 = 2.3  =) căn 6 = căn 2 . căn 3)

=) 5 + 2 căn 6 = (căn 2 + căn 3)²

 8 + 2 căn 15 = 5 + 2 căn 15 + 3 = (căn 5 + căn 3)²

 tự giải nhé