Tính : a) \(\sqrt {\dfrac{{25}}{{64}}} \);
b) \(\sqrt {\dfrac{{16}}{{25}}:\dfrac{{49}}{{64}}} \);
c) \(\dfrac{{\sqrt {63} }}{{\sqrt 7 }}\).
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\(a)\;\;\sqrt {\dfrac{{25}}{{64}}} = \dfrac{{\sqrt {25} }}{{\sqrt {64} }} = \dfrac{{\left| 5 \right|}}{{\left| 8 \right|}} = \dfrac{5}{8}.\) \(c)\;\;\dfrac{{\sqrt {63} }}{{\sqrt 7 }} = \sqrt {\dfrac{{63}}{7}} = \sqrt 9 = \sqrt {{3^2}} = \left| 3 \right| = 3.\)
\(b)\;\sqrt {\dfrac{{16}}{{25}}:\dfrac{{49}}{{64}}} = \sqrt {\dfrac{{16.64}}{{25.49}}} = \dfrac{{\sqrt {16} .\sqrt {64} }}{{\sqrt {25} .\sqrt {49} }} = \dfrac{{\sqrt {{4^2}} .\sqrt {{8^2}} }}{{\sqrt {{5^2}} .\sqrt {{7^2}} }} = \dfrac{{\left| 4 \right|.\left| 8 \right|}}{{\left| 5 \right|.\left| 7 \right|}} = \dfrac{{4.8}}{{5.7}} = \dfrac{{32}}{{35}}.\)