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

Toán Lớp 9: $\frac{căn của (2+căn3)}{căn 2}$ Tính ạ

Toán Lớp 9: $\frac{căn của (2+căn3)}{căn 2}$
Tính ạ

Comments ( 2 )

  1. (\sqrt{2+\sqrt{3}})/(\sqrt{2})
    =(\sqrt{2}.(\sqrt{2+\sqrt{3}}))/(\sqrt{2}.\sqrt{2})
    =(\sqrt{4+2\sqrt{3}})/(2)
    =(\sqrt{(\sqrt{3})^2+2.\sqrt{3}.1+1^2})/(2)
    =(\sqrt{(\sqrt{3}+1)^2})/(2)
    =(|\sqrt{3}+1|)/(2)
    =(\sqrt{3}+1)/(2)
     

  2. $\frac{\sqrt[2]{2 + \sqrt[2]{3}}}{\sqrt[2]{2}}$
    = $\frac{(\sqrt[2]{2 + \sqrt[2]{3}}).\sqrt[2]{2}}{\sqrt[2]{2}.\sqrt[2]{2}}$
    = $\frac{\sqrt[2]{4 + 2\sqrt[2]{3}}}{2}$ 
    = $\frac{\sqrt[2]{3 + 2\sqrt[2]{3} + 1}}{2}$ 
    = $\frac{(\sqrt[2]{3} + 1)²}{2}$ 
    = $\frac{|\sqrt[2]{3} + 1|}{2}$ 
    = $\frac{\sqrt[2]{3} + 1}{2}$ 
     

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