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Giải bài tập 3.17 trang 59 SGK Toán 9 tập 1 - Kết nối tri thức

Đưa thừa số ra ngoài dấu căn: a) (sqrt {52} ;) b) (sqrt {27a} left( {a ge 0} right);) c) (sqrt {50sqrt 2 + 100} ;) d) (sqrt {9sqrt 5 - 18} .)

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

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Đề bài

Đưa thừa số ra ngoài dấu căn: a) \(\sqrt {52} ;\) b) \(\sqrt {27a} \left( {a \ge 0} \right);\) c) \(\sqrt {50\sqrt 2  + 100} ;\) d) \(\sqrt {9\sqrt 5  - 18} .\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

♊Ta có \(\sqrt {{A^2}B}  = \left| A \right|.\sqrt B \)

Lời giải chi tiết

a) \(\sqrt {52}  = \sqrt {4.13}  = \sqrt {{2^2}.13}  = 2\sqrt {13} \) b) \(\sqrt {27a}  = \sqrt {9.3a}  = \sqrt {{3^2}.3a}  = 3\sqrt {3a} \) c) \(\sqrt {50\sqrt 2  + 100} \)\( = \sqrt {25.2\sqrt 2  + 25.4} \)\( = \sqrt {25\left( {2\sqrt 2  + 4} \right)} \)\( = 5\sqrt {2\sqrt 2  + 4} \) d) \(\sqrt {9\sqrt 5  - 18}  = \sqrt {9\left( {\sqrt 5  - 2} \right)}  = 3\sqrt {\sqrt 5  - 2} \)

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