Giải bài 4 trang 67 vở thực hành Toán 9

Rút gọn các biểu thức sau a) (sqrt[3]{{{{left( { - x - 1} right)}^3}}}); b) (sqrt[3]{{8{x^3} - 12{x^2} + 6x - 1}}).

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

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Đề bài

Rút gọn các biểu thức sau a) \(\sqrt[3]{{{{\left( { - x - 1} \right)}^3}}}\); b) \(\sqrt[3]{{8{x^3} - 12{x^2} + 6x - 1}}\).

Phương pháp giải - Xem chi tiết

Ta có \({\left( {\sqrt[3]{A}} \right)^3} = \sqrt[3]{{{A^3}}} = A\) với A là một biểu thức đại số.

Lời giải chi tiết

a) \(\sqrt[3]{{{{\left( { - x - 1} \right)}^3}}} = - x - 1\); b) Có \(8{x^3} - 12{x^2} + 6x - 1 = {\left( {2x - 1} \right)^3}\) nên \(\sqrt[3]{{8{x^3} - 12{x^2} + 6x - 1}} = \sqrt[3]{{{{\left( {2x - 1} \right)}^3}}} = 2x - 1\).

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4.9 trên 7 phiếu

ﷺ Giải bài 5 trang 67 vở thực hành Toán 9 Xét căn thức (sqrt[3]{{27{x^3} - 27{x^2} + 9x - 1}}). a) Viết biểu thức trong dấu căn dưới dạng một lập phương. b) Tính giá trị của biểu thức (A = {x^2} - x + 3 - sqrt[3]{{27{x^3} - 27{x^2} + 9x - 1}}) tại (x = 2,1).
♛ Giải bài 6 trang 67 vở thực hành Toán 9 Chiều dài đường xích đạo của Trái Đất có thể ước tính theo thể tích V của Trái Đất bằng công thức (C = sqrt[3]{{6V{pi ^2}}}). Cho biết Trái Đất có thể tích khoảng 1 083 207 300 000(k{m^3}). Chiều dài đường xích đạo của Trái Đất bằng bao nhiêu km (làm tròn kết quả đến hàng đơn vị)?
ಞ Giải bài 3 trang 66 vở thực hành Toán 9 Giả sử lực F của gió khi thổi theo phương vuông góc với bề mặt cánh buồm của một con thuyền tỉ lệ thuận với bình phương tốc độ của gió, hệ số tỉ lệ là 30. Trong đó, lực F được tính bằng N (Newton) và tốc độ được tính bằng m/s. a) Khi tốc độ của gió là 10m/s thì lực F là bao nhiêu Newton? b) Nếu cánh buồm chỉ có thể chịu được một áp lực tối đa là 12 000N thì con thuyền đó có thể đi được trong gió với tốc độ gió tối đa là bao nhiêu?
ꦰ Giải bài 2 trang 66 vở thực hành Toán 9 Tính giá trị của các biểu thức sau: a) (3sqrt {45} + frac{{5sqrt {15} }}{{sqrt 3 }} - 2sqrt {245} ); b) (frac{{sqrt {12} - sqrt 4 }}{{sqrt 3 - 1}} - frac{{sqrt {21} + sqrt 7 }}{{sqrt 3 + 1}} + sqrt 7 ); c) (frac{{3 - sqrt 3 }}{{1 - sqrt 3 }} + sqrt 3 left( {2sqrt 3 - 1} right) + sqrt {12} ); d) (frac{{sqrt 3 - 1}}{{sqrt 2 }} + frac{{sqrt 2 }}{{sqrt 3 - 1}} - frac{6}{{sqrt 6 }}).
𝔉 Giải bài 1 trang 65 vở thực hành Toán 9 Rút gọn các biểu thức sau: a) (frac{{5 + 3sqrt 5 }}{{sqrt 5 }} - frac{1}{{sqrt 5 - 2}}); b) (sqrt {{{left( {sqrt 7 - 2} right)}^2}} - sqrt {63} + frac{{sqrt {56} }}{{sqrt 2 }}); c) (frac{{sqrt {{{left( {sqrt 3 + sqrt 2 } right)}^2}} + sqrt {{{left( {sqrt 3 - sqrt 2 } right)}^2}} }}{{2sqrt {12} }}); d) (frac{{sqrt[3]{{{{left( {sqrt 2 + 1} right)}^3}}} - 1}}{{sqrt {50} }}).

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Luyện Bài Tập Trắc nghiệm Toán 9 - Kết nối tri thức - Xem ngay

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