12 bài tập Rút gọn biểu thức chứa căn bậc ba có lời giải

Đáp án đúng là: A

$\frac{{\sqrt[3]{2}}}{{\sqrt[3]{2} - 1}} - \sqrt[3]{4} - \sqrt[3]{2} = \frac{{\sqrt[3]{2}\left( {\sqrt[3]{{{2^2}}} + \sqrt[3]{2} + 1} \right)}}{{\left( {\sqrt[3]{2} - 1} \right)\left( {\sqrt[3]{{{2^2}}} + \sqrt[3]{2} + 1} \right)}} - \sqrt[3]{4} - \sqrt[3]{2}$

$= 2 + \sqrt[3]{4} + \sqrt[3]{2} - \sqrt[3]{4} - \sqrt[3]{2} = 2$.

Đáp án đúng là: A

Ta có: $\sqrt[3]{{\left( {\sqrt 2 + 1} \right)\left( {3 + 2\sqrt 2 } \right)}} = \sqrt[3]{{\left( {\sqrt 2 + 1} \right){{\left( {1 + \sqrt 2 } \right)}^2}}} = \sqrt[3]{{{{\left( {\sqrt 2 + 1} \right)}^3}}} = \sqrt 2 + 1$.

Đáp án đúng là: A

Ta có: $\sqrt[3]{{ - 343}}.\sqrt[3]{3} + \sqrt[3]{{81}} - 2\sqrt[3]{{24}} = - 7\sqrt[3]{3} + 3.3\sqrt[3]{3} - 2\sqrt[3]{3} = 0$.

Đáp án đúng là: C

Ta có:

$2\sqrt[3]{{24}} - 3\sqrt[3]{{81}} + 4\sqrt[3]{{192}} - 2\sqrt[3]{{375}}$

$= 2\sqrt[3]{{8.3}} - 3\sqrt[3]{{27.3}} + 4\sqrt[3]{{64.3}} - 2\sqrt[3]{{125.3}}$

$= 2.2\sqrt[3]{3} - 3.3\sqrt[3]{3} + 4.4\sqrt[3]{3} - 2.5.\sqrt[3]{3}$

$= 4\sqrt[3]{3} - 9\sqrt[3]{3} + 16\sqrt[3]{3} - 10.\sqrt[3]{3} = \sqrt[3]{3}$.

Đáp án đúng là: D

Ta có:

$\left( {\sqrt[3]{9} - \sqrt[3]{6} + \sqrt[3]{4}} \right)\left( {\sqrt[3]{3} + \sqrt[3]{2}} \right)$

$= \sqrt[3]{9}.\sqrt[3]{3} - \sqrt[3]{6}.\sqrt[3]{3} + \sqrt[3]{4}.\sqrt[3]{3} + \sqrt[3]{9}.\sqrt[3]{2} - \sqrt[3]{6}.\sqrt[3]{2} + \sqrt[3]{4}.\sqrt[3]{2}$

$= \sqrt[3]{{{3^3}}} + \sqrt[3]{{18}} - \sqrt[3]{{18}} - \sqrt[3]{{12}} + \sqrt[3]{{12}} + \sqrt[3]{{{2^3}}}$

$= 3 + 2 = 5$.