Tính và so sánh : a) \(\sqrt {\dfrac{{100}}{4}} \) và \(\dfrac{{\sqrt {100} }}{{\sqrt 4 }}\)
b) \(\sqrt {\dfrac{{400}}{{25}}} \)và \(\dfrac{{\sqrt {400} }}{{\sqrt {25} }}\).
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\(\begin{array}{l}a)\;\;\sqrt {\dfrac{{100}}{4}} = \sqrt {25} = \sqrt {{5^2}} = \left| 5 \right| = 5;\;\;\dfrac{{\sqrt {100} }}{{\sqrt 4 }} = \dfrac{{\sqrt {{{10}^2}} }}{{\sqrt {{2^2}} }} = \dfrac{{\left| {10} \right|}}{{\left| 2 \right|}} = \dfrac{{10}}{2} = 5.\\ \Rightarrow \sqrt {\dfrac{{100}}{4}} = \dfrac{{\sqrt {100} }}{{\sqrt 4 }}\;\;\left( { = 5} \right).\\b)\;\sqrt {\dfrac{{400}}{{25}}} = \sqrt {16} = \sqrt {{4^2}} = \left| 4 \right| = 4;\;\;\dfrac{{\sqrt {400} }}{{\sqrt {25} }} = \dfrac{{\sqrt {{{20}^2}} }}{{\sqrt {{5^2}} }} = \dfrac{{\left| {20} \right|}}{{\left| 5 \right|}} = \dfrac{{20}}{5} = 4.\\ \Rightarrow \sqrt {\dfrac{{400}}{{25}}} = \dfrac{{\sqrt {400} }}{{\sqrt {25} }}\;\;\;\left( { = 4} \right).\end{array}\)