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Lý thuyết Căn thức bậc hai và căn thức bậc ba của biểu thức đại số Toán 9 Cánh diều

1. Căn thức bậc hai Khái niệm căn thức bậc hai Với A là một biểu thức đại số, người ta gọi \(\sqrt A \) là căn thức bậc hai của A, còn A được gọi là biểu thức lấy căn bậc hai hay biểu thức dưới dấu căn.

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

Toán - Văn - Anh
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1. Căn thức bậc hai

Khái niệm căn thức bậc hai

Với A là một biểu thức đại số, người ta gọi \(\sqrt A \) là căn thức bậc hai ꦍcủa A, còn A được gọi là biểu thức lấy căn bậc hai hay biểu thức dưới dấu căn.

Ví dụ: \(\sqrt {2x - 1} \)🐈, \(\sqrt { - \frac{1}{3}{x^2} + 2} \) là các căn thức bậc hai.

Điều kiện xác định của căn thức bậc hai

Điều kiện xác định cho căn thức bậc hai \(\sqrt A \) là \(A \ge 0\).

Ví dụ: ღĐiều kiện xác định của căn thức \(\sqrt {2x + 1} \) là \(2x + 1 \ge 0\) hay \(x \ge  - \frac{1}{2}\).

Điều kiện xác định của căn thức \(\sqrt { - \frac{1}{3}x + 2} \) là \( - \frac{1}{3}x + 2 \ge 0\) hay \(x \le 6\).

2. Căn thức bậc ba

Khái niệm căn thức bậc ba

Với A là một biểu thức đại số, người ta gọi \(\sqrt[3]{A}\) là căn thức bậc ba🌼 của A, còn A được gọi là biểu thức lấy căn bậc ba hay biểu thức dưới dấu căn.

Chú ý: Các số, biến số được nối với nhau bởi dấu các phép tính cộng, trừ, nhân, chia, nâng lên lũy thừa, khai căn (bậc hai hay bậc ba) làm thành một biểu thức đại số.

Ví dụ: \(\sqrt[3]{x}\)⛎, \(\sqrt[3]{{\frac{1}{{x + 1}}}}\) là các căn thức bậc ba.

Điều kiện xác định của căn thức bậc ba

Điều kiện xác định cho căn thức bậc ba \(\sqrt[3]{A}\) chính là điều kiện xác định của biểu thức A.

Ví dụ:

\(\sqrt[3]{{5x - 11}}\) xác định với mọi số thực x vì \(5x - 11\) xác định với mọi số thực x.\(\sqrt[3]{{\frac{1}{{x - 1}}}}\) xác định với \(x \ne 1\) vì \(\frac{1}{{x - 1}}\) xác định với \(x \ne 1\).

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