Rút gọn
a) \(\sqrt {\dfrac{{2{a^2}{b^4}}}{{50}}} \) b) \(\dfrac{{\sqrt {2a{b^2}} }}{{\sqrt {162} }}\) với \(a \ge 0.\)
Sử dụng các công thức \(\sqrt {\dfrac{A}{B}} = \dfrac{{\sqrt A }}{{\sqrt B }}\,\left( {A \ge 0;B > 0} \right)\); \(\sqrt {AB} = \sqrt A .\sqrt B ;\,\sqrt {{A^2}} = \left| A \right|.\)
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a) Ta có \(\sqrt {\dfrac{{2{a^2}{b^4}}}{{50}}} = \sqrt {\dfrac{{{a^2}{b^4}}}{{25}}} = \dfrac{{\sqrt {{a^2}{b^4}} }}{{\sqrt {25} }} = \dfrac{{\sqrt {{a^2}} .\sqrt {{b^4}} }}{5} = \dfrac{{a{b^2}}}{5}\)
b) Ta có \(\dfrac{{\sqrt {2a{b^2}} }}{{\sqrt {162} }} = \sqrt {\dfrac{{2a{b^2}}}{{162}}} = \sqrt {\dfrac{{a{b^2}}}{{81}}} = \dfrac{{\sqrt {a{b^2}} }}{{\sqrt {81} }} = \dfrac{{\sqrt a .\sqrt {{b^2}} }}{9} = \dfrac{{\left| b \right|\sqrt a }}{9}\)