Giải:

\(A=1-\dfrac{5}{\sqrt{196}}-\dfrac{5}{\left(2.\sqrt{21}\right)^2}-\dfrac{\sqrt{25}}{204}-\dfrac{\left(\sqrt{5}\right)^2}{374}\)

\(\Leftrightarrow A=1-\dfrac{5}{14}-\dfrac{5}{2^2.\left(\sqrt{21}\right)^2}-\dfrac{5}{204}-\dfrac{5}{374}\)

\(\Leftrightarrow A=1-\dfrac{5}{14}-\dfrac{5}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)

\(\Leftrightarrow A=\dfrac{5}{5}-\dfrac{5}{14}-\dfrac{5}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)

\(\Leftrightarrow A=5\left(\dfrac{1}{5}-\dfrac{1}{14}-\dfrac{1}{84}-\dfrac{1}{204}-\dfrac{1}{374}\right)\)

\(\Leftrightarrow A=5.\dfrac{6}{55}\)

\(\Leftrightarrow A=\dfrac{6}{11}\)

Vậy giá trị của biểu thức A là \(\dfrac{6}{11}\).

Chúc bạn học tốt!

a: \(A=\dfrac{1-\dfrac{1}{\sqrt{49}}+\dfrac{1}{49}-\dfrac{1}{\left(7\sqrt{7}\right)^2}}{\dfrac{\sqrt{64}}{2}-\dfrac{4}{7}+\left(\dfrac{2}{7}\right)^2-\dfrac{4}{343}}\)

\(=\dfrac{1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}}{4-\dfrac{4}{7}+\dfrac{4}{49}-\dfrac{4}{343}}\)

\(=\dfrac{1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}}{4\left(1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}\right)}=\dfrac{1}{4}\)

b: \(M=1-\dfrac{5}{\sqrt{196}}-\dfrac{5}{\left(2\sqrt{21}\right)^2}-\dfrac{\sqrt{25}}{204}-\dfrac{\left(\sqrt{5}\right)^2}{374}\)

\(=1-\dfrac{5}{14}-\dfrac{5}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)

\(=1-5\left(\dfrac{1}{14}+\dfrac{1}{84}+\dfrac{1}{204}+\dfrac{1}{374}\right)\)

\(=1-5\left(\dfrac{1}{2\cdot7}+\dfrac{1}{7\cdot12}+\dfrac{1}{12\cdot17}+\dfrac{1}{17\cdot22}\right)\)

\(=1-\left(\dfrac{5}{2\cdot7}+\dfrac{5}{7\cdot12}+\dfrac{5}{12\cdot17}+\dfrac{5}{17\cdot22}\right)\)

\(=1-\left(\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{22}\right)\)

\(=1-\left(\dfrac{1}{2}-\dfrac{1}{22}\right)\)

\(=1-\dfrac{11-1}{22}=1-\dfrac{10}{22}=\dfrac{12}{22}=\dfrac{6}{11}\)

\(M=1-\dfrac{5}{14}-\dfrac{5}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)

\(=\dfrac{84-30-5}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)

\(=\dfrac{49}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)

\(=\dfrac{7}{12}-\dfrac{5}{204}-\dfrac{5}{374}\)

\(=\dfrac{7\cdot17-5}{204}-\dfrac{5}{374}=\dfrac{19}{34}-\dfrac{5}{374}=\dfrac{204}{374}=\dfrac{6}{11}\)

\(M=1-\frac{5}{\sqrt{196}}-\frac{5}{\left(2\sqrt{21}\right)^2}-\frac{\sqrt{25}}{204}-\frac{\left(\sqrt{5}\right)^2}{374}\)

\(=1-\frac{5}{14}-\frac{5}{84}-\frac{5}{204}-\frac{5}{374}\left(\text{(}2\sqrt{21}\text{)}^2=2^2.21=84\right)\)

\(=1-\frac{5}{2.7}-\frac{5}{7.12}-\frac{5}{12.17}-\frac{5}{17.22}\)

\(=1-\frac{1}{2}+\frac{1}{7}-\frac{1}{7}+\frac{1}{12}-\frac{1}{12}+\frac{1}{17}-\frac{1}{17}+\frac{1}{22}\)

\(=1-\frac{1}{2}+\frac{1}{22}\)

\(=\frac{22-11+1}{22}=\frac{12}{22}=\frac{6}{11}\)

Vậy M = 6/11.