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Giải bài 3 trang 8 sách bài tập toán 11 - Chân trời sáng tạo tập 2

Tính giá trị của các biểu thức sau:

꧑Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Tính giá trị của các biểu thức sau: a) \(\sqrt[4]{{125}}.\sqrt[4]{5}\); b) \(\frac{{\sqrt[4]{{243}}}}{{\sqrt[4]{3}}}\); c) \(\frac{{\sqrt[3]{3}}}{{\sqrt[3]{{24}}}}\); d) \(\sqrt {\sqrt[3]{{64}}} \); e) \(\sqrt[4]{{3\sqrt[3]{3}}}\); g) \({\left( { - \sqrt[6]{4}} \right)^3}\).

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về phép tính căn bậc n để tính: a) \(\sqrt[n]{a}.\sqrt[n]{b} = \sqrt[n]{{ab}}\) b, c) \(\frac{{\sqrt[n]{a}}}{{\sqrt[n]{b}}} = \sqrt[n]{{\frac{a}{b}}}\) với \(b \ne 0\) d, e) \(\sqrt[m]{{\sqrt[n]{a}}} = \sqrt[{mn}]{a}\) g) \({\left( {\sqrt[n]{a}} \right)^m} = \sqrt[n]{{{a^m}}}\)

Lời giải chi tiết

a) \(\sqrt[4]{{125}}.\sqrt[4]{5} = \sqrt[4]{{{5^3}.5}} = \sqrt[4]{{{5^4}}} = 5\); b) \(\frac{{\sqrt[4]{{243}}}}{{\sqrt[4]{3}}} = \sqrt[4]{{\frac{{243}}{3}}} = \sqrt[4]{{81}} = \sqrt[4]{{{3^4}}} = 3\); c) \(\frac{{\sqrt[3]{3}}}{{\sqrt[3]{{24}}}} = \sqrt[3]{{\frac{3}{{24}}}} = \sqrt[3]{{\frac{1}{{{2^3}}}}} = \frac{1}{2}\); d) \(\sqrt {\sqrt[3]{{64}}}  = \sqrt[{3.2}]{{64}} = \sqrt[6]{{{2^6}}} = 2\); e) \(\sqrt[4]{{3\sqrt[3]{3}}} = \sqrt[4]{{\sqrt[3]{{{3^3}.3}}}} = \sqrt[3]{3}\); g) \({\left( { - \sqrt[6]{4}} \right)^3} =  - \sqrt[6]{{{4^3}}} =  - \sqrt[6]{{{{\left( {{2^2}} \right)}^3}}} =  - \sqrt[6]{{{2^6}}} =  - 2\).

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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