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

Đề bài

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

Lời giải chi tiết

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

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

$e)\;\sqrt {7 – 4\sqrt 3 }  – \sqrt[3]{{26 + 15\sqrt 3 }}$

$= \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}}}$

$= \sqrt {{{\left( {2 – \sqrt 3 } \right)}^2}}  – \sqrt[3]{{{{\left( {2 + \sqrt 3 } \right)}^3}}}\\ = \left| {2 – \sqrt 3 } \right| – \left( {2 + \sqrt 3 } \right)$

$= 2 – \sqrt 3  – 2 – \sqrt 3  =  – 2\sqrt 3 .$

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