\(\sqrt{\dfrac{1}{600}}=\sqrt{\dfrac{1\cdot6}{600\cdot6}}=\sqrt{\dfrac{6}{60^2}}=\dfrac{\sqrt{6}}{60}\)

\(\sqrt{\dfrac{11}{540}}=\sqrt{\dfrac{11\cdot15}{540\cdot15}}=\sqrt{\dfrac{165}{90^2}}=\dfrac{\sqrt{165}}{90}\)

\(\sqrt{\dfrac{3}{50}}=\sqrt{\dfrac{3\cdot2}{50\cdot2}}=\sqrt{\dfrac{6}{10^2}}=\dfrac{\sqrt{6}}{10}\)

\(\sqrt{\dfrac{5}{98}}=\sqrt{\dfrac{5\cdot2}{98\cdot2}}=\sqrt{\dfrac{10}{12^2}}=\dfrac{\sqrt{10}}{12}\)

\(\sqrt{\dfrac{\left(1-\sqrt{3}\right)^2}{27}}=\sqrt{\dfrac{3\left(1-\sqrt{3}\right)^2}{27\cdot3}}\)

\(=\dfrac{\sqrt{3\left(1-\sqrt{3}\right)^2}}{\sqrt{9^2}}=\dfrac{\left|1-\sqrt{3}\right|\cdot\sqrt{3}}{9}\)

\(=\dfrac{\left(\sqrt{3}-1\right)\sqrt{3}}{9}\)

\(x^4-99x^2-100=0\)

\(\Leftrightarrow x^4-100x^2+x^2-100=0\)

<=>\(\left(x^2+10\right)\left(x^2-10\right)+\left(x-10\right)\left(x+10\right)=0\)\(\Leftrightarrow x\left(x+10\right)\left(x-10\right)+\left(x+10\right)\left(x-10\right)=0\)\(\Leftrightarrow\left(x+10\right)\left(x-10\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-10=0\\x+10=0\\x+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-10\\x=-1\end{matrix}\right.\)

vậy tập nghiệm của pt là S={10;-10;-1}

\(\dfrac{R_1}{R_2}=\dfrac{S_2}{S_1}\Rightarrow\dfrac{R_1}{R_2}=\dfrac{30}{10}=3\)

R1=3R2

\(\sqrt{79x}=\sqrt{79}\cdot\sqrt{x}\)