Bài 2 trang 36 Tài liệu dạy – học Toán 9 tập 1: Tính...

Tính :

a) $\sqrt[3]{{64}} - \sqrt[3]{{ - 125}} - 2\sqrt[3]{{216}}$;       

b) $\sqrt[3]{{81}} + 3\sqrt[3]{{24}} - 2\sqrt[3]{{375}}$;

c) $\dfrac{{\sqrt[3]{{135}}}}{{\sqrt[3]{5}}} - \sqrt[3]{{54}}.\sqrt[3]{4}$;   

d) $\sqrt[3]{{54x{y^3}}} - y\sqrt[3]{{128x}}$;

e) $\sqrt {7 - 4\sqrt 3 }  - \sqrt[3]{{26 + 15\sqrt 3 }}$.

+) Sử dụng công thức: $\sqrt[3]{{ab}} = \sqrt[3]{a}.\sqrt[3]{b},\;\;\sqrt[3]{{\dfrac{a}{b}}} = \dfrac{{\sqrt[3]{a}}}{{\sqrt[3]{b}}}\;\;\left( {b \ne 0} \right).$

$\begin{array}{l}a)\;\sqrt[3]{{64}} - \sqrt[3]{{ - 125}} - 2\sqrt[3]{{216}}\\ = \sqrt[3]{{{4^3}}} - \sqrt[3]{{{{\left( { - 5} \right)}^3}}} - 2\sqrt[3]{{{6^3}}}\\ = 4 - \left( { - 5} \right) - 2.6\\ =  - 3.\end{array}$                                       $\begin{array}{l}b)\;\sqrt[3]{{81}} + 3\sqrt[3]{{24}} - 2\sqrt[3]{{375}}\\ = \sqrt[3]{{{{3.3}^3}}} + 3\sqrt[3]{{{{3.2}^3}}} - 2\sqrt[3]{{{{3.5}^3}}}\\ = 3\sqrt[3]{3} + 3.2\sqrt[3]{3} - 2.5\sqrt[3]{3}\\ =  - \sqrt[3]{3}.\end{array}$

$\begin{array}{l}c)\;\dfrac{{\sqrt[3]{{135}}}}{{\sqrt[3]{5}}} - \sqrt[3]{{54}}.\sqrt[3]{4}\\ = \sqrt[3]{{\dfrac{{135}}{5}}} - \sqrt[3]{{54.4}}\\ = \sqrt[3]{{27}} - \sqrt[3]{{216}}\\ = \sqrt[3]{{{3^3}}} - \sqrt[3]{{{6^3}}}\\ = 3 - 6 =  - 3.\end{array}$                                                           $\begin{array}{l}d)\;\sqrt[3]{{54x{y^3}}} - y\sqrt[3]{{128x}}\\ = \sqrt[3]{{{{2.3}^3}x{y^3}}} - y\sqrt[3]{{{{2.4}^3}x}}\\ = 3y\sqrt[3]{{2x}} - 4y\sqrt[3]{{2x}}\\ =  - y\sqrt[3]{{2x}}\end{array}$

$\begin{array}{l}e)\;\sqrt {7 - 4\sqrt 3 }  - \sqrt[3]{{26 + 15\sqrt 3 }}\\ = \sqrt {4 - 2.2.\sqrt 3  + {{\left( {\sqrt 3 } \right)}^2}}  - \sqrt[3]{{{2^3} + {{3.2}^2}\sqrt 3  + 3.2.{{\left( {\sqrt 3 } \right)}^2} + {{\left( {\sqrt 3 } \right)}^3}}}\\ = \sqrt {{{\left( {2 - \sqrt 3 } \right)}^2}}  - \sqrt[3]{{{{\left( {2 + \sqrt 3 } \right)}^3}}}\\ = \left| {2 - \sqrt 3 } \right| - \left( {2 + \sqrt 3 } \right)\\ = 2 - \sqrt 3  - 2 - \sqrt 3  =  - 2\sqrt 3 .\end{array}$