$\frac{ √2+ √3+ √6+ √8+ √16}{√2+ √3+ √4 }$

Question

$\frac{ √2+ √3+ √6+ √8+ √16}{√2+ √3+ √4 }$

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Valentina 2 tháng 2021-10-01T23:28:49+00:00 2 Answers 9 views 0

Answers ( )

    0
    2021-10-01T23:30:17+00:00

    \(\dfrac{\sqrt 2+\sqrt3+\sqrt 6+\sqrt 8+4}{\sqrt2+\sqrt 3+\sqrt 4}\)

    \(=\dfrac{\sqrt 2+\sqrt3+2+\sqrt 6+\sqrt 8+2}{\sqrt2+\sqrt 3+\sqrt 4}\)

    \(=\dfrac{\sqrt 2+\sqrt3+\sqrt 4+\sqrt 6+\sqrt 8+\sqrt 4}{\sqrt2+\sqrt 3+\sqrt 4}\)

    \(=1+\dfrac{\sqrt 2(\sqrt3+\sqrt4+\sqrt2)}{\sqrt2+\sqrt 3+\sqrt 4}\)

    \(=1+1\)

    \(=2\)

    0
    2021-10-01T23:30:33+00:00

    $\frac{√2+√3+√6+√8+√16}{√2+√3+√4}$

     =$\frac{√2+√3+√6+√8+4}{√2+√3+√4}$

    =$\frac{√2+√3+2}{√2+√3+√4}$ +$\frac{2+√6+√8}{√2+√3+√4}$ 

    =1+$\frac{√2(√2+√3+√4)}{√2+√3+√4}$ 

    =1+√2

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