Đề bài
Tính :
a] \[\sqrt {\dfrac{{25}}{{64}}} \];
b] \[\sqrt {\dfrac{{16}}{{25}}:\dfrac{{49}}{{64}}} \];
c] \[\dfrac{{\sqrt {63} }}{{\sqrt 7 }}\].
Lời giải chi tiết
\[a]\;\;\sqrt {\dfrac{{25}}{{64}}} = \dfrac{{\sqrt {25} }}{{\sqrt {64} }} = \dfrac{{\left| 5 \right|}}{{\left| 8 \right|}} = \dfrac{5}{8}.\]
\[b]\;\sqrt {\dfrac{{16}}{{25}}:\dfrac{{49}}{{64}}} = \sqrt {\dfrac{{16.64}}{{25.49}}} \]
\[\; = \dfrac{{\sqrt {16} .\sqrt {64} }}{{\sqrt {25} .\sqrt {49} }} = \dfrac{{\sqrt {{4^2}} .\sqrt {{8^2}} }}{{\sqrt {{5^2}} .\sqrt {{7^2}} }} \]
\[\;= \dfrac{{\left| 4 \right|.\left| 8 \right|}}{{\left| 5 \right|.\left| 7 \right|}} = \dfrac{{4.8}}{{5.7}} = \dfrac{{32}}{{35}}.\]
\[c]\;\;\dfrac{{\sqrt {63} }}{{\sqrt 7 }} = \sqrt {\dfrac{{63}}{7}} = \sqrt 9 = \sqrt {{3^2}}\]\[\, = \left| 3 \right| = 3.\]