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Giải bài tập 3.7 trang 51 SGK Toán 9 tập 1 - Kết nối tri thức

Tính: a) (sqrt {12} .left( {sqrt {12} + sqrt 3 } right);) b) (sqrt 8 .left( {sqrt {50} - sqrt 2 } right);) c) ({left( {sqrt 3 + sqrt 2 } right)^2} - 2sqrt 6 .)

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Đề bài

Tính: a) \(\sqrt {12} .\left( {\sqrt {12}  + \sqrt 3 } \right);\) b) \(\sqrt 8 .\left( {\sqrt {50}  - \sqrt 2 } \right);\) c) \({\left( {\sqrt 3  + \sqrt 2 } \right)^2} - 2\sqrt 6 .\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức \(\sqrt A .\sqrt B  = \sqrt {A.B} \)

Lời giải chi tiết

a) \(\sqrt {12} .\left( {\sqrt {12}  + \sqrt 3 } \right)\) \(\begin{array}{l} = \sqrt {12} .\sqrt {12}  + \sqrt {12} .\sqrt 3 \\ = \sqrt {{{12}^2}} +\sqrt {36} \\ = 12+6\\ = 18\end{array}\) b) \(\sqrt 8 .\left( {\sqrt {50}  - \sqrt 2 } \right)\) \(\begin{array}{l} = \sqrt 8 .\sqrt {50}  - \sqrt 8 .\sqrt 2 \\ = \sqrt {400}  - \sqrt {16} \\ = 20 - 4\\ = 16\end{array}\) c) \({\left( {\sqrt 3  + \sqrt 2 } \right)^2} - 2\sqrt 6 \) \(\begin{array}{l} = {\sqrt 3 ^2} + 2.\sqrt 3 .\sqrt 2  + {\sqrt 2 ^2} - 2\sqrt 6 \\ = 3 + 2\sqrt 6  + 2 - 2\sqrt 6 \\ = 5\end{array}\)

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