Tính:a) \({\mkern 1mu} {\mkern 1mu} \sqrt {\dfrac{{289}}{{225}}} \)b) \({\mkern 1mu} {\mkern 1mu} \sqrt
Tính:
a) \({\mkern 1mu} {\mkern 1mu} \sqrt {\dfrac{{289}}{{225}}} \)
b) \({\mkern 1mu} {\mkern 1mu} \sqrt {2\dfrac{{14}}{{25}}} \)
c) \({\mkern 1mu} {\mkern 1mu} \sqrt {\dfrac{{0,25}}{9}} \)
d) \({\mkern 1mu} {\mkern 1mu} \sqrt {1\dfrac{9}{{16}}.5\dfrac{4}{9}.0,01} \)
e) \({\mkern 1mu} {\mkern 1mu} \sqrt {\dfrac{{{{149}^2} - {{76}^2}}}{{{{457}^2} - {{384}^2}}}} \)
Áp dụng phép khai phương một thương.
a) \(\sqrt {\dfrac{{289}}{{225}}} = \dfrac{{\sqrt {289} }}{{\sqrt {225} }} = \dfrac{{\sqrt {{{17}^2}} }}{{\sqrt {{{15}^2}} }} = \dfrac{{17}}{{15}}\).
b) \(\sqrt {2\dfrac{{14}}{{25}}} = \sqrt {\dfrac{{64}}{{25}}} = \dfrac{{\sqrt {64} }}{{\sqrt {25} }} = \dfrac{{\sqrt {{8^2}} }}{{\sqrt {{5^2}} }} = \dfrac{8}{5}\).
c) \(\sqrt {\dfrac{{0,25}}{9}} = \dfrac{{\sqrt {0,25} }}{{\sqrt 9 }} = \dfrac{{\sqrt {0,{5^2}} }}{{\sqrt {{3^2}} }} = \dfrac{{0,5}}{3} = \dfrac{1}{6}\).
d) \(\sqrt {1\dfrac{9}{{16}} \cdot 5\dfrac{4}{9} \cdot 0,01} = \sqrt {\dfrac{{25}}{{16}} \cdot \dfrac{{49}}{9} \cdot \dfrac{1}{{100}}} \)
\( = \sqrt {\dfrac{{25}}{{16}}} \cdot \sqrt {\dfrac{{49}}{9}} \cdot \sqrt {\dfrac{1}{{100}}} = \sqrt {\dfrac{{{5^2}}}{{{4^2}}}} \cdot \sqrt {\dfrac{{{7^2}}}{{{3^2}}}} \cdot \sqrt {\dfrac{1}{{{{10}^2}}}} = \dfrac{5}{4} \cdot \dfrac{7}{3} \cdot \dfrac{1}{{10}} = \dfrac{7}{{24}}\).
e) \(\sqrt {\dfrac{{{{149}^2} - {{76}^2}}}{{{{457}^2} - {{384}^2}}}} = \sqrt {\dfrac{{\left( {149 - 76} \right)\left( {149 + 76} \right)}}{{\left( {457 - 384} \right)\left( {457 + 384} \right)}}} \)
\( = \sqrt {\dfrac{{73.225}}{{73.841}}} = \sqrt {\dfrac{{225}}{{841}}} = \dfrac{{\sqrt {225} }}{{\sqrt {841} }} = \dfrac{{15}}{{29}}\).
Hỗ trợ - Hướng dẫn
-
024.7300.7989
-
1800.6947
(Thời gian hỗ trợ từ 7h đến 22h)
Email: lienhe@tuyensinh247.com