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Giải bài tập 3 trang 72 SGK Toán 9 tập 1 - Cánh diều

Rút gọn biểu thức: a. (A = sqrt {40_{}^2 - 24_{}^2} ); b. (B = left( {sqrt {12} + 2sqrt 3 - sqrt {27} } right).sqrt 3 ); c. (C = frac{{sqrt {63_{}^3 + 1} }}{{sqrt {63_{}^2 - 62} }}); d. (D = sqrt {60} - 5sqrt {frac{3}{5}} - 3sqrt {frac{5}{3}} ).

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

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Đề bài

Rút gọn biểu thức: a. \(A = \sqrt {40_{}^2 - 24_{}^2} \); b. \(B = \left( {\sqrt {12}  + 2\sqrt 3  - \sqrt {27} } \right).\sqrt 3 \); c. \(C = \frac{{\sqrt {63_{}^3 + 1} }}{{\sqrt {63_{}^2 - 62} }}\); d. \(D = \sqrt {60}  - 5\sqrt {\frac{3}{5}}  - 3\sqrt {\frac{5}{3}} \).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Áp dụng các kiến thức về căn bậc hai của một thương, căn bâc hai của một tích, đưa thừa số vào trong căn bậc hai và đưa thừa số ra ngoài căn bậc hai để giải bài toán.

Lời giải chi tiết

a. \(A = \sqrt {40_{}^2 - 24_{}^2} \) \(\begin{array}{l} = \sqrt {\left( {40 - 24} \right)\left( {40 + 24} \right)} \\ = \sqrt {16.64}  = \sqrt {16} .\sqrt {64} \\ = 4.8 = 32\end{array}\) b. \(B = \left( {\sqrt {12}  + 2\sqrt 3  - \sqrt {27} } \right).\sqrt 3 \) \(\begin{array}{l} = \left( {2\sqrt 3  + 2\sqrt 3  - 3\sqrt 3 } \right).\sqrt 3 \\ = \sqrt 3.\sqrt 3 \\ = 3\end{array}\) c. \(C = \frac{{\sqrt {{{63}^3} + 1} }}{{\sqrt {{{63}^2} - 62} }}\) \(\begin{array}{l} = \frac{{\sqrt {\left( {63 + 1} \right)\left( {63_{}^2 - 63 + 1} \right)} }}{{\sqrt {63_{}^2 - 62} }}\\ = \frac{{\sqrt {64.\left( {63_{}^2 - 62} \right)} }}{{\sqrt {63_{}^2 - 62} }}\\ = \frac{{\sqrt {64} .\sqrt {63_{}^2 - 62} }}{{\sqrt {63_{}^2 - 62} }}\\ = \sqrt {64} \\ = 8\end{array}\) d. \(D = \sqrt {60}  - 5\sqrt {\frac{3}{5}}  - 3\sqrt {\frac{5}{3}} \) \(\begin{array}{l} = \sqrt {4.15}  - \sqrt {5^2.\frac{3}{5}}  - \sqrt {3^2.\frac{5}{3}}\\ = 2\sqrt {15}- \sqrt {15} - \sqrt {15}\\ = 0\end{array}\)

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