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Giải bài 1 trang 53 vở thực hành Toán 9

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

Toán - Văn - Anh
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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) \({\left( {\sqrt 3  + \sqrt 2 } \right)^2} - 2\sqrt 6 \).

Phương pháp giải - Xem chi tiết

Với A, B là các biểu thức không âm, ta có: \(\sqrt A .\sqrt B  = \sqrt {AB} \).

Lời giải chi tiết

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

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