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\(\sqrt{\left(3-\sqrt{5}\right)^2}=\left|3-\sqrt{5}\right|=3-\sqrt{5}\)
\(\sqrt{\left(\sqrt{3-\sqrt{4}}\right)^2}=\left|\sqrt{3-\sqrt{4}}\right|=\sqrt{3-\sqrt{4}}\)
\(\sqrt{\left(7-\sqrt{34}\right)^2}=\left|7-\sqrt{34}\right|=7-\sqrt{34}\)
\(0,\left(34\right)=0\left(01\right).34=\dfrac{1}{99}\)
\(0,\left(5\right)=0,\left(1\right).5=\dfrac{1}{9}.5=\dfrac{5}{9}\)
\(0,\left(123\right)=0,\left(001\right).123=\dfrac{1}{999}.123=\dfrac{123}{999}=\dfrac{41}{333}\)
a: \(=0.5\cdot10-\dfrac{1}{7}+15=20-\dfrac{1}{7}=\dfrac{139}{7}\)
b: \(=6\cdot\dfrac{-2}{3}+12\cdot\dfrac{4}{9}+18\cdot\dfrac{-8}{27}\)
\(=-4+\dfrac{16}{3}-\dfrac{16}{3}=-4\)
c: \(=\left(\dfrac{5}{2}+\dfrac{3}{8}-\dfrac{5}{8}+\dfrac{2}{3}\right):\left(\dfrac{17}{2}+\dfrac{49}{4}-\dfrac{17}{8}+\dfrac{34}{15}\right)\)
\(=\dfrac{35}{12}:\dfrac{2507}{120}=\dfrac{350}{2507}\)
\(A=\frac{15}{34}+\frac{7}{21}+\frac{9}{34}-1\frac{15}{17}+\frac{2}{3}=\frac{15}{34}+\frac{7}{21}+\frac{9}{34}-\frac{64}{34}+\frac{14}{21}=\left(\frac{15}{34}+\frac{9}{34}-\frac{64}{34}\right)+\left(\frac{7}{21}+\frac{14}{21}\right)=\frac{30}{34}+\frac{21}{21}=\frac{15}{17}+1=\frac{32}{17}\)
34,(59)=34,60 ; \(\sqrt{5}\)=2,24