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Lý thuyết Căn bậc ba Toán 9 Chân trời sáng tạo

1. Căn bậc ba của một số Khái niệm căn bậc ba của một số thực

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

Toán - Văn - Anh
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1. Căn bậc ba của một số

Khái niệm căn bậc ba của một số thực

- Cho số thực a. Số thực x thỏa mãn \({x^3} = a\) được gọi là căn bậc ba của a.

- Mỗi số thực a đều có đúng một căn bậc ba, kí hiệu là \(\sqrt[3]{a}\).

Trong kí hiệu \(\sqrt[3]{a}\), số 3 được gọi là chỉ số căn. Phép toán tìm căn bậc ba của một số gọi là phép khai căn bậc hai.

Chú ý:ℱ Từ định nghĩa căn bậc ba, ta có \({\left( {\sqrt[3]{a}} \right)^3} = \sqrt[3]{{{a^3}}} = a\).

Ví dụ:

\(\sqrt[3]{{64}} = \sqrt[3]{{{4^3}}} = 4\);\(\sqrt[3]{{ - 27}} = \sqrt[3]{{{{\left( { - 3} \right)}^3}}} =  - 3\).

2. Tính căn bậc ba của một số bằng máy tính cầm tay

Ta có thể sử dụng loại MTCT thích hợp để tính căn bậc ba của một số.

Ví dụ:

3. Căn thức bậc ba

Khái niệm

Với A là một biểu thức đại số, ta gọi \(\sqrt[3]{A}\) là căn thức bậc ba của A.

Ví dụ:🌠 Với \(x = 60\), giá trị của \(\sqrt[3]{{2x + 5}}\) là:

\(\sqrt[3]{{2.60 + 5}} = \sqrt[3]{{125}} = \sqrt[3]{{{5^3}}} = 5\).

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