Khử mẫu của biểu thức lấy căn:
a) \(\sqrt {\frac{{10}}{{11}}} \)
b) \(\sqrt {\frac{{42}}{{300}}} \)
c) \(\sqrt {\frac{{5a}}{{12b}}} (a \ge 0;b > 0)\)
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Dựa vào: \(\frac{{\sqrt a }}{{\sqrt b }} = \frac{{\sqrt a .\sqrt b }}{{{{\left( {\sqrt b } \right)}^2}}} = \frac{{\sqrt {ab} }}{b}(a \ge 0,b > 0)\)
\(\sqrt {\frac{a}{b}} = \sqrt {\frac{{ab}}{{{b^2}}}} = \frac{{\sqrt {ab} }}{b}(a \ge 0,b > 0)\)
a) \(\sqrt {\frac{{10}}{{11}}} = \frac{{\sqrt {10} .\sqrt {11} }}{{\sqrt {11} .\sqrt {11} }} = \frac{{\sqrt {110} }}{{11}}\).
b) \(\sqrt {\frac{{42}}{{300}}} = \sqrt {\frac{{14}}{{100}}} = \frac{{\sqrt {14} }}{{10}}\).
c) \(\sqrt {\frac{{5a}}{{12b}}} = \sqrt {\frac{{5a3b}}{{4.3b.3b}}} = \sqrt {\frac{{15ab}}{{{2^2}{{.3}^2}b{}^2}}} = \frac{{\sqrt {15ab} }}{{6b}}(a \ge 0;b > 0)\).