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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 9: căn( 5 + 2 căn 6) – căn (5-2 căn 6)

Toán Lớp 9: căn( 5 + 2 căn 6) – căn (5-2 căn 6)

Comments ( 2 )

  1. \sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}
    =\sqrt{2+2.\sqrt{2}.\sqrt{3}+3}-\sqrt{3-2.\sqrt{3}.\sqrt{2}+2}
    =\sqrt{(\sqrt{2}+\sqrt{3})^2}-\sqrt{(\sqrt{3}-\sqrt{2})^2}
    =|\sqrt{2}+\sqrt{3}|-|\sqrt{3}-\sqrt{2}|
    =\sqrt{2}+\sqrt{3}-\sqrt{3}+\sqrt{2}
    =2\sqrt{2}
     

  2. \text{Giải đáp+ Lời giải và giải thích chi tiết:}
    \sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}
    =\sqrt{3+2\sqrt{3*2}+2}-\sqrt{3-2\sqrt{3*2}+2
    =\sqrt{(\sqrt{3}+\sqrt{2})^2}-\sqrt{(\sqrt{3}-\sqrt{2})^2}
    =|\sqrt{3}+\sqrt{2}|-|\sqrt{3}-\sqrt{2}|
    =\sqrt{3}+\sqrt{2}-(\sqrt{3}-\sqrt{2})
    =\sqrt{3}+\sqrt{2}-\sqrt{3}+\sqrt{2}
    =2\sqrt{2}

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222-9+11+12:2*14+14 = ? ( )