a) \(\sqrt{\dfrac{25}{81}.\dfrac{16}{49}.\dfrac{196}{9}}=\sqrt{\left(\dfrac{5}{9}\right)^2.\left(\dfrac{4}{7}\right)^2.\left(\dfrac{14}{3}\right)^2}=\dfrac{5}{9}.\dfrac{4}{7}.\dfrac{14}{3}=\dfrac{40}{27}\)
b) \(\sqrt{3\dfrac{1}{16}.2\dfrac{14}{25}.2\dfrac{34}{81}}=\sqrt{\dfrac{49}{16}.\dfrac{64}{25}.\dfrac{196}{81}}=\sqrt{\left(\dfrac{7}{4}\right)^2.\left(\dfrac{8}{5}\right)^2.\left(\dfrac{14}{9}\right)^2}\)
\(=\dfrac{7}{4}.\dfrac{8}{5}.\dfrac{14}{9}=\dfrac{196}{45}\)
c) \(\dfrac{\sqrt{640}.\sqrt{34,3}}{\sqrt{567}}=\sqrt{\dfrac{640.34,3}{567}}=\sqrt{\dfrac{7.3136}{7.81}}=\sqrt{\dfrac{3136}{81}}=\sqrt{\left(\dfrac{56}{9}\right)^2}=\dfrac{56}{9}\)
d) \(\sqrt{21,6}.\sqrt{810}.\sqrt{11^2-5^2}=\sqrt{21,6.810}.\sqrt{\left(11-5\right)\left(11+5\right)}=\sqrt{36.6.81}.\sqrt{6.16}=6.9\sqrt{6}.4\sqrt{6}=1296\)
a) Ta có: \(\sqrt{\dfrac{25}{81}\cdot\dfrac{16}{49}\cdot\dfrac{169}{9}}\)
\(=\dfrac{5}{9}\cdot\dfrac{4}{7}\cdot\dfrac{13}{3}\)
\(=\dfrac{260}{189}\)
b) Ta có: \(\sqrt{3\dfrac{1}{16}\cdot2\dfrac{14}{25}\cdot2\dfrac{34}{81}}\)
\(=\sqrt{\dfrac{49}{16}\cdot\dfrac{64}{25}\cdot\dfrac{196}{81}}\)
\(=\dfrac{7}{4}\cdot\dfrac{8}{5}\cdot\dfrac{14}{9}\)
\(=\dfrac{196}{45}\)
c) Ta có: \(\sqrt{\dfrac{640\cdot34.3}{567}}\)
\(=\sqrt{\dfrac{21952}{567}}\)
\(=\sqrt{\dfrac{3136}{81}}=\dfrac{56}{9}\)
d) Ta có: \(\sqrt{21.6}\cdot\sqrt{810}\cdot\sqrt{11^2-5^2}\)
\(=\sqrt{21.6\cdot810}\cdot\sqrt{96}\)
\(=54\sqrt{6}\cdot4\sqrt{6}\)
\(=1296\)
