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Giải bài 3.15 trang 36 sách bài tập toán 9 - Kết nối tri thức tập 1

Tính giá trị biểu thức (P = {left( {sqrt {20} + 2sqrt {45} - 3sqrt {80} } right)^2}).

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

Toán - Văn - Anh
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Đề bài

Tính giá trị biểu thức \(P = {\left( {\sqrt {20}  + 2\sqrt {45}  - 3\sqrt {80} } \right)^2}\).

Phương pháp giải - Xem chi tiết

Nếu a là một số và b là một số không âm thì \(\sqrt {{a^2}.b}  = \left| a \right|\sqrt b \).

Lời giải chi tiết

\(P = {\left( {\sqrt {20}  + 2\sqrt {45}  - 3\sqrt {80} } \right)^2} \\= {\left( {\sqrt {{2^2}.5}  + 2\sqrt {{3^2}.5}  - 3\sqrt {{4^2}.5} } \right)^2} \\= {\left( {2\sqrt 5  + 6\sqrt 5  - 12\sqrt 5 } \right)^2}\\= {\left( { - 4\sqrt 5 } \right)^2} = 16.5 = 80\)

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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