Bài 6:
a) \(x^2-5=0\\ \Rightarrow x^2=5\\ \Rightarrow x=\pm\sqrt{5}\)
b) \(x^2-\dfrac{14}{25}=0\\ \Rightarrow x^2=\dfrac{14}{25}\\ \Rightarrow x=\pm\sqrt{\dfrac{14}{25}}\)
c) \(\left(x-\sqrt{2}\right)^2=2\\ \Rightarrow\left[{}\begin{matrix}x-\sqrt{2}=-\sqrt{2}\\x-\sqrt{2}=\sqrt{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=2\sqrt{2}\end{matrix}\right.\)
d) \(\left(2x-3\sqrt{5}\right)^2=5\\ \Rightarrow\left[{}\begin{matrix}2x-3\sqrt{5}=-\sqrt{5}\\2x-3\sqrt{5}=\sqrt{5}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=2\sqrt{5}\\2x=4\sqrt{5}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\sqrt{5}\\x=2\sqrt{5}\end{matrix}\right.\)
Bài 1:
a) \(0,\left(21\right)=\dfrac{7}{33}\)
b) \(0,0\left(123\right)=\dfrac{41}{3330}\)
c) \(0,00\left(24\right)=\dfrac{2}{825}\)
Bài 5:
a) \(-4\sqrt{\dfrac{4}{25}}+7\sqrt{0,16}+6\sqrt{0,04}-0\sqrt{2003}=-4.\dfrac{2}{5}+7.\dfrac{2}{5}+6.\dfrac{1}{5}-0=-\dfrac{8}{5}+\dfrac{14}{5}+\dfrac{6}{5}=\dfrac{12}{5}\)
b) \(\dfrac{\sqrt{36}}{\sqrt{25}}.\dfrac{1}{4}-\dfrac{\sqrt{49}}{\sqrt{64}}.\dfrac{\sqrt{36}}{\sqrt{25}}=\dfrac{6}{5}.\dfrac{1}{4}-\dfrac{7}{8}.\dfrac{6}{5}=\dfrac{6}{5}.-\dfrac{5}{8}=-\dfrac{3}{4}\)
c) \(\sqrt{12100}=110\)
d) \(\sqrt{\dfrac{49}{400}}=\dfrac{7}{20}\)
e) \(4\sqrt{5}+3\sqrt{20}-2\sqrt{80}=4\sqrt{5}+3.\sqrt{4}.\sqrt{5}-2.\sqrt{16}.\sqrt{5}=4\sqrt{5}+6\sqrt{5}-8\sqrt{5}=2\sqrt{5}\)
f) \(12\sqrt{3}-5\sqrt{27}-7\sqrt{12}=12\sqrt{3}-5.\sqrt{9}.\sqrt{3}-7.\sqrt{4}.\sqrt{3}=12\sqrt{3}-15\sqrt{3}-14\sqrt{3}=-17\sqrt{3}\)
Bài 5:
a: \(-4\sqrt{\dfrac{4}{25}}+7\sqrt{0.16}+6\sqrt{0.04}-0\sqrt{2003}\)
\(=-4\cdot\dfrac{2}{5}+7\cdot\dfrac{2}{5}+6\cdot\dfrac{1}{5}\)
\(=-\dfrac{8}{5}+\dfrac{14}{5}+\dfrac{6}{5}\)
\(=\dfrac{12}{5}\)
b: \(\dfrac{\sqrt{36}}{\sqrt{25}}\cdot\dfrac{1}{4}-\dfrac{\sqrt{49}}{\sqrt{64}}\cdot\dfrac{\sqrt{36}}{\sqrt{25}}\)
\(=\dfrac{6}{5}\cdot\dfrac{1}{4}-\dfrac{7}{8}\cdot\dfrac{6}{5}\)
\(=\dfrac{6}{5}\cdot\dfrac{-5}{8}=-\dfrac{3}{4}\)
