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Trả lời:
a) Ta có: \[\sqrt {1\frac{9}{{16}}.5\frac{4}{5}.0,01} = \sqrt {\frac{{25}}{{16}}} .\sqrt {\frac{{49}}{9}} .\sqrt {0,01} = \frac{5}{4}.\frac{7}{3}.0,1 = \frac{7}{{24}}\].
b) Ta có \[\sqrt {1,44.1,21 - 1,44.0,4} = \sqrt {1,44.\left( {1,21 - 0,4} \right)} \]
\[ = \sqrt {1,44.0,81} = \sqrt {1,44} .\sqrt {0,81} = 1,2.0,9 = 1,08\].
c) Ta có: \[\sqrt {\frac{{{{165}^2} - {{124}^2}}}{{164}}} = \sqrt {\frac{{\left( {165 - 124} \right)\left( {165 + 124} \right)}}{{164}}} = \sqrt {\frac{{41.289}}{{164}}} = \sqrt {\frac{{289}}{4}} = \frac{{17}}{2}\].
d) \[\sqrt {\frac{{{{149}^2} - {{76}^2}}}{{{{457}^2} - {{384}^2}}}} = \sqrt {\frac{{73.225}}{{73.841}}} = \frac{{\sqrt {225} }}{{\sqrt {841} }} = \frac{{15}}{{29}}\].
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