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Giải bài 9 trang 53 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Rút gọn biểu thức (sqrt {245} - sqrt {75} + sqrt {45} - sqrt {12} ) nhận được biểu thức có dạng (asqrt 5 + bsqrt 3 ). Giá trị của a – b là A. 17 B. 3 C. 9 D. 10

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

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Đề bài

Rút gọn biểu thức \(\sqrt {245}  - \sqrt {75}  + \sqrt {45}  - \sqrt {12} \) nhận được biểu thức có dạng \(a\sqrt 5  + b\sqrt 3 \). Giá trị của a – b là A. 17 B. 3 C. 9 D. 10

Phương pháp giải - Xem chi tiết

Dựa vào: Với hai số thực a và b không âm, ta có \(\sqrt {a.b}  = \sqrt a .\sqrt b \).

Lời giải chi tiết

\(\begin{array}{l}\sqrt {245}  - \sqrt {75}  + \sqrt {45}  - \sqrt {12} \\ = \sqrt {49.5}  - \sqrt {25.3}  + \sqrt {9.5}  - \sqrt {4.3} \\ = 7\sqrt 5  - 5\sqrt 3  + 3\sqrt 5  - 2\sqrt 3 \\ = 10\sqrt 5  - 7\sqrt 3 \end{array}\) Vậy với biểu thức có dạng \(a\sqrt 5  + b\sqrt 3 \) ta được a = 10; b = - 7 Suy ra a – b = 10 – (-7) = 17. Chọn đáp án A.

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

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