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Giải bài 11 trang 57 sách bài tập toán 9 - Cánh diều tập 1

Áp dụng quy tắc về căn bậc hai của một bình phương, hãy tính: a) \(\sqrt {{2^2}.{{\left( { - 9} \right)}^2}} \) b) \(\sqrt {{{\left( {\sqrt {11} - 4} \right)}^2}} \) c) \(\sqrt {{{\left( {\frac{1}{{\sqrt 2 }} - \frac{1}{{\sqrt 3 }}} \right)}^2}} \) d) \(\sqrt {9 + 4\sqrt 5 } \)

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

Toán - Văn - Anh
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Đề bài

Áp dụng quy tắc về căn bậc hai của một bình phương, hãy tính: a)    \(\sqrt {{2^2}.{{\left( { - 9} \right)}^2}} \) b)   \(\sqrt {{{\left( {\sqrt {11}  - 4} \right)}^2}} \) c)    \(\sqrt {{{\left( {\frac{1}{{\sqrt 2 }} - \frac{1}{{\sqrt 3 }}} \right)}^2}} \) d)   \(\sqrt {9 + 4\sqrt 5 } \)

Phương pháp giải - Xem chi tiết

Áp dụng: Với mọi số a, ta có \(\sqrt {{a^2}}  = \left| a \right|\)

Lời giải chi tiết

a)   \(\sqrt {{2^2}.{{\left( { - 9} \right)}^2}}  = \sqrt {{2^2}{{.9}^2}}  = \sqrt {{{18}^2}}  = 18\) b)   \(\sqrt {{{\left( {\sqrt {11}  - 4} \right)}^2}}  = \left| {\sqrt {11}  - 4} \right| = 4 - \sqrt {11} \) (do \(4 > \sqrt {11} \)). c)   \(\sqrt {{{\left( {\frac{1}{{\sqrt 2 }} - \frac{1}{{\sqrt 3 }}} \right)}^2}}  = \left| {\frac{1}{{\sqrt 2 }} - \frac{1}{{\sqrt 3 }}} \right| = \frac{1}{{\sqrt 2 }} - \frac{1}{{\sqrt 3 }}\) (do \(\frac{1}{{\sqrt 2 }} > \frac{1}{{\sqrt 3 }}\)) d)  \(\sqrt {9 + 4\sqrt 5 }  = \sqrt {{2^2} + 2.2.\sqrt 5  + {{\left( {\sqrt 5 } \right)}^2}} \) \(= \sqrt {{{\left( {2 + \sqrt 5 } \right)}^2}}  = \left| {2 + \sqrt 5 } \right| = 2 + \sqrt 5 .\)

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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