d: Ta có: \(\sqrt{6+\sqrt{11}}-\sqrt{6-\sqrt{11}}\)

\(=\dfrac{\sqrt{12+2\sqrt{11}}-\sqrt{12-2\sqrt{11}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{11}+1-\sqrt{11}+1}{\sqrt{2}}\)

\(=\sqrt{2}\)

a)

\(7\sqrt{12}+\frac{1}{3}\sqrt{27}-\sqrt{75}\)

\(=14\sqrt{3}+\sqrt{3}-5\sqrt{3}\)

\(=10\sqrt{3}\)

b)

\(\left(2\sqrt{20}+\sqrt{125}-3\sqrt{80}\right):5\)

\(=\left(4\sqrt{5}+5\sqrt{5}-12\sqrt{5}\right):5\)

\(=-3\sqrt{5}:5\)

\(=\frac{-3\sqrt{5}}{5}\)

c)

\(3\sqrt{12a}-5\sqrt{3a}+\sqrt{48a}\)

\(=6\sqrt{3a}-5\sqrt{3a}+4\sqrt{3a}\)

\(=5\sqrt{3a}\)

đk: \(x\ge0\)

Ta có: \(\sqrt{x}+2\sqrt{x+3}=x+4\)

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

\(\Leftrightarrow\sqrt{\left(\sqrt{x-3}-1\right)^2}=\sqrt{x}-1\)

\(\Leftrightarrow\left|\sqrt{x-3}-1\right|=\sqrt{x}-1\)

\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x-3}-1=\sqrt{x}-1\\\sqrt{x-3}-1=1-\sqrt{x}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x-3}=\sqrt{x}\left(ktm\right)\\\sqrt{x-3}+\sqrt{x}=2\end{cases}}\)

\(\Leftrightarrow x-3+x+2\sqrt{x\left(x-3\right)}=4\)

\(\Leftrightarrow2\sqrt{x^2-3x}=7-2x\)

\(\Leftrightarrow4\left(x^2-3x\right)=\left(7-2x\right)^2\)

\(\Leftrightarrow4x^2-12x=49-28x+4x^2\)

\(\Leftrightarrow16x=49\)

\(\Rightarrow x=\frac{49}{16}\)

\(( \sqrt{x+3}-1)^2\) chứ bạn.

với cả là \(\sqrt{x+3}\)  mà   có phải \(\sqrt{x-3} \)  đâu

ĐKXĐ:\(x>-3\)

\(\sqrt{x}+\sqrt{x+3}=x+4\)\(\Leftrightarrow x+x+3+2\sqrt{x}\sqrt{x+3}=\left(x+4\right)^2\)

\(\Leftrightarrow2x+3+2\sqrt{x^2+3x}=x^2+8x+16\)

\(\Leftrightarrow x^2+8x+16-2x-3-2\sqrt{x^2+3x}=0\)

\(\Leftrightarrow\left(x^2+3x-2\sqrt{x^2+3x}+1\right)+3x+12=0\)

\(\Leftrightarrow\left(\sqrt{x^2+3x}-1\right)^2+3\left(x+4\right)=0\)

Ta thấy:\(\hept{\begin{cases}\left(\sqrt{x^2+3x}-1\right)^2\ge0\\x>-3\Leftrightarrow3\left(x+4\right)>0\end{cases}}\)

\(\Rightarrow\left(\sqrt{x^2+3x}-1\right)^2+3\left(x+4\right)>0\)

\(\Leftrightarrow x\in\varnothing\)

Vậy phương trình vô nghiệm.

\(\sqrt{x+4\sqrt{x-1}+3}-\sqrt{4x+4\sqrt{x-1}-3}=1\)(đk:\(1\le x< 2\)) Lý do có điều kiện này là nhờ vào việc VT=1>0

\(\Leftrightarrow\sqrt{\left(x-1\right)+4\sqrt{x-1}+4}-\sqrt{4\left(x-1\right)+4\sqrt{x-1}+1}=1\)

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

\(\Leftrightarrow\left(\sqrt{x-1}+2\right)-\left(2\sqrt{x-1}+1\right)=1\)

\(\Leftrightarrow\sqrt{x-1}=0\)

\(\Leftrightarrow x=1\)(thõa mãn điều kiện)

Ta có : \(\sqrt{x+4\sqrt{x-1}+3}-\sqrt{4x+4\sqrt{x-1}-3}=1\) ( ĐK : \(x\ge1\) )

\(\Leftrightarrow\sqrt{\left(x-1\right)+4\sqrt{x-1}+4}-\sqrt{4.\left(x-1\right)+4.\sqrt{x-1}+1}=1\)

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

\(\Leftrightarrow\left|\sqrt{x-1}+2\right|-\left|2\sqrt{x-1}+1\right|=1\)

\(\Leftrightarrow\sqrt{x-1}+2-2\sqrt{x-1}-1=1\)

\(\Leftrightarrow\sqrt{x-1}=0\)

\(\Leftrightarrow x-1=0\)

\(\Leftrightarrow x=1\) ( Thỏa mãn )

     2\(\sqrt{\dfrac{16}{3}}\)  - 3\(\sqrt{\dfrac{1}{27}}\) - \(\dfrac{3}{2\sqrt{3}}\)

= \(\dfrac{8}{\sqrt{3}}\) - \(\dfrac{3}{3\sqrt{3}}\)  - \(\dfrac{3}{2\sqrt{3}}\)

= \(\dfrac{8}{\sqrt{3}}\) - \(\dfrac{1}{\sqrt{3}}\) - \(\dfrac{3}{2\sqrt{3}}\)

= \(\dfrac{16}{2\sqrt{3}}\) - \(\dfrac{2}{2\sqrt{3}}\) - \(\dfrac{3}{2\sqrt{3}}\)

= \(\dfrac{11}{2\sqrt{3}}\)

= \(\dfrac{11\sqrt{3}}{6}\)

f, 2\(\sqrt{\dfrac{1}{2}}\)- \(\dfrac{2}{\sqrt{2}}\) + \(\dfrac{5}{2\sqrt{2}}\)

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

= \(\dfrac{5}{2\sqrt{2}}\)

= \(\dfrac{5\sqrt{2}}{4}\)

(1 + \(\dfrac{3-\sqrt{3}}{\sqrt{3}-1}\)).(1- \(\dfrac{3+\sqrt{3}}{\sqrt{3}+1}\)) 

= \(\dfrac{\sqrt{3}-1+3-\sqrt{3}}{\sqrt{3}-1}\).\(\dfrac{\sqrt{3}+1-3+\sqrt{3}}{\sqrt{3}+1}\)

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

= \(\dfrac{-4}{3-1}\)

= \(\dfrac{-4}{2}\)

= -2

Mình cần gấp nha mn 😭😭 

1) Ta có: \(\frac{x+6\sqrt{x}+9}{x-9}=\frac{\left(\sqrt{x}+3\right)^2}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\frac{\sqrt{x}+3}{\sqrt{x}-3}\)