Toán Lớp 9: √2+√3+√6+√8+√16/√2+√3+2 rút g9n
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Toán Lớp 9: √2+√3+√6+√8+√16/√2+√3+2 rút g9n
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\dfrac{{\sqrt 2 + \sqrt 3 + \sqrt 6 + \sqrt 8 + \sqrt {16} }}{{\sqrt 2 + \sqrt 3 + 2}}\\
= \dfrac{{\sqrt 2 + \sqrt 3 + 4 + \sqrt 6 + \sqrt 8 }}{{\sqrt 2 + \sqrt 3 + 2}}\\
= \dfrac{{\sqrt 2 + \sqrt 3 + 2 + 2 + \sqrt 2 .\sqrt 3 + 2\sqrt 2 }}{{\sqrt 2 + \sqrt 3 + 2}}\\
= \dfrac{{\sqrt 2 + \sqrt 3 + 2 + \sqrt 2 .\left( {\sqrt 2 + \sqrt 3 + 2} \right)}}{{\sqrt 2 + \sqrt 3 + 2}}\\
= \dfrac{{\left( {\sqrt 2 + \sqrt 3 + 2} \right)\left( {1 + \sqrt 2 } \right)}}{{\sqrt 2 + \sqrt 3 + 2}}\\
= 1 + \sqrt 2
\end{array}$