a) \(\sqrt[]{x^2-4x+4}=x+3\)

\(\Leftrightarrow\sqrt[]{\left(x-2\right)^2}=x+3\)

\(\Leftrightarrow\left|x-2\right|=x+3\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=x+3\\x-2=-\left(x+3\right)\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}0x=5\left(loại\right)\\x-2=-x-3\end{matrix}\right.\)

\(\Leftrightarrow2x=-1\Leftrightarrow x=-\dfrac{1}{2}\)

b) \(2x^2-\sqrt[]{9x^2-6x+1}=5\)

\(\Leftrightarrow2x^2-\sqrt[]{\left(3x-1\right)^2}=5\)

\(\Leftrightarrow2x^2-\left|3x-1\right|=5\)

\(\Leftrightarrow\left|3x-1\right|=2x^2-5\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-1=2x^2-5\\3x-1=-2x^2+5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}2x^2-3x-4=0\left(1\right)\\2x^2+3x-6=0\left(2\right)\end{matrix}\right.\)

Giải pt (1)

\(\Delta=9+32=41>0\)

Pt \(\left(1\right)\) \(\Leftrightarrow x=\dfrac{3\pm\sqrt[]{41}}{4}\)

Giải pt (2)

\(\Delta=9+48=57>0\)

Pt \(\left(2\right)\) \(\Leftrightarrow x=\dfrac{-3\pm\sqrt[]{57}}{4}\)

Vậy nghiệm pt là \(\left[{}\begin{matrix}x=\dfrac{3\pm\sqrt[]{41}}{4}\\x=\dfrac{-3\pm\sqrt[]{57}}{4}\end{matrix}\right.\)

Theo bài ra ta có

\(\sqrt{0,04}\)+\(\dfrac{3}{5}\)-\(\sqrt{0.25}\)+\(\dfrac{113}{10}\)

=0,2+0,6-0,5+11,3

=0,8-0,5+11,3

=0,3+11,3

=11,6

a) Ta có: \(\dfrac{2}{\sqrt{3}-1}+\dfrac{3}{\sqrt{3}-2}+\dfrac{12}{3-\sqrt{3}}\)

\(=\dfrac{2\left(\sqrt{3}+1\right)}{2}-\dfrac{3\left(2+\sqrt{3}\right)}{1}+\dfrac{12\left(3+\sqrt{3}\right)}{6}\)

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

\(=-2\sqrt{3}-5+6+2\sqrt{3}\)

=1

b) Ta có: \(\dfrac{1}{\sqrt{3}-\sqrt{2}}-\dfrac{2}{\sqrt{7}+\sqrt{5}}-\dfrac{3}{\sqrt{5}-\sqrt{2}}+\dfrac{4}{\sqrt{7}+\sqrt{3}}\)

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

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

a: \(=9\sqrt{2}-4\sqrt{2}+4\sqrt{2}+9\sqrt{2}=18\sqrt{2}\)

b: \(=8\sqrt{3}-12\sqrt{3}+5\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)

c: \(=2\sqrt{21}\)

1) \(3\sqrt{2}-4\sqrt{18}+2\sqrt{32}-\sqrt{50}\)

\(=3\sqrt{2}-12\sqrt{2}+8\sqrt{2}-5\sqrt{2}\)

\(=-6\sqrt{2}\)

2) \(\sqrt{50}-\sqrt{18}+\sqrt{200}-\sqrt{162}\)

\(=5\sqrt{2}-3\sqrt{2}+10\sqrt{2}-9\sqrt{2}\)

\(=3\sqrt{2}\)

3) \(5\sqrt{5}+\sqrt{20}-3\sqrt{45}\)

\(=5\sqrt{5}+2\sqrt{5}-9\sqrt{5}\)

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

4) \(5\sqrt{48}-4\sqrt{27}-2\sqrt{75}+\sqrt{108}\)

\(=20\sqrt{3}-12\sqrt{3}-10\sqrt{3}+6\sqrt{3}\)

\(=4\sqrt{3}\)

5) \(\dfrac{1}{2}\sqrt{48}-2\sqrt{75}-\dfrac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\dfrac{1}{3}}\)

\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\dfrac{10}{3}\sqrt{3}\)

\(=-\dfrac{17}{3}\sqrt{3}\)