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Giải bài tập 3.21 trang 59 SGK Toán 9 tập 1 - Kết nối tri thức

Rút gọn các biểu thức sau: a) (2sqrt {frac{2}{3}} - 4sqrt {frac{3}{2}} ;) b) (frac{{5sqrt {48} - 3sqrt {27} + 2sqrt {12} }}{{sqrt 3 }};) c) (frac{1}{{3 + 2sqrt 2 }} + frac{{4sqrt 2 - 4}}{{2 - sqrt 2 }}.)

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

Toán - Văn - Anh
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Đề bài

Rút gọn các biểu thức sau: a) \(2\sqrt {\frac{2}{3}}  - 4\sqrt {\frac{3}{2}} ;\) b) \(\frac{{5\sqrt {48}  - 3\sqrt {27}  + 2\sqrt {12} }}{{\sqrt 3 }};\) c) \(\frac{1}{{3 + 2\sqrt 2 }} + \frac{{4\sqrt 2  - 4}}{{2 - \sqrt 2 }}.\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

✱Sử dụng trục căn thức để khử mẫu, đưa thừa số ra ngoài dấu căn và đưa vào trong dấu căn, kết hợp các phương pháp để rút gọn biểu thức

Lời giải chi tiết

a) \(2\sqrt {\frac{2}{3}}  - 4\sqrt {\frac{3}{2}} \)\( = 2\frac{{\sqrt 2 }}{{\sqrt 3 }} - 4\frac{{\sqrt 3 }}{{\sqrt 2 }}\)\( = 2.\frac{{\sqrt 6 }}{3} - 4.\frac{{\sqrt 6 }}{2}\)\( = \sqrt 6 \left( {\frac{2}{3} - 2} \right)\)\( = \frac{{ - 4\sqrt 6 }}{3}.\) b) \(\frac{{5\sqrt {48}  - 3\sqrt {27}  + 2\sqrt {12} }}{{\sqrt 3 }}\)\( = \frac{{5\sqrt {16.3}  - 3\sqrt {9.3}  + 2\sqrt {4.3} }}{{\sqrt 3 }}\)\( = \frac{{\sqrt 3 .\left( {5\sqrt {16}  - 3\sqrt 9  + 2\sqrt 4 } \right)}}{{\sqrt 3 }}\)\( = 5.4 - 3.3 + 2.2\)\( = 20 - 9 + 4\)\( = 15\) c) \(\frac{1}{{3 + 2\sqrt 2 }} + \frac{{4\sqrt 2  - 4}}{{2 - \sqrt 2 }}\)\( = \frac{{3 - 2\sqrt 2 }}{{\left( {3 + 2\sqrt 2 } \right)\left( {3 - 2\sqrt 2 } \right)}} + \frac{{4\left( {\sqrt 2  - 1} \right)}}{{\sqrt 2 \left( {\sqrt 2  - 1} \right)}}\)\( = \frac{{3 - 2\sqrt 2 }}{{9 - 8}} + \frac{4}{{\sqrt 2 }}\)\( = 3 - 2\sqrt 2  + \frac{{4\sqrt 2 }}{2}\) \( = 3 - 2\sqrt 2  + 2\sqrt 2 \)\( = 3\)

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